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Date:     Sat, 28 Jan 95 16:37:11 PST
From: "Karrenbach, Martin Horst"  <EN.FOL@Forsythe.Stanford.EDU>
To: martin@sep.stanford.edu
Subject:  INSPEC display (Find TITLE CENTRAL LIMIT THEOREM...)
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INSPEC / Search: Find TITLE CENTRAL LIMIT THEOREM
Result: 31 citations

Citation 1 --------------------------------------------------------------------
TITLE:         A central limit theorem for absorbing Markov chains with r
                 absorbing states.
AUTHOR:        Al-Eideh, B.M. (Dept. of Math. Sci., Jordan Univ. of Sci. &
                 Technol., Irbid, Jordan)
PUBLICATION:   Journal of Information & Optimization Sciences (Sept. 1994)
                 vol.15, no.3, p. 387-92. (ISSN 0252-2667) 6 refs.
LOCATION:      Stanford
                 Publication not found in Socrates.  Type HELP LOCATION.
DOCUMENT TYPE: Journal article
LANGUAGE:      English
ABSTRACT:  A central limit theorem is obtained for a sequence of random
   variables defined on a finite absorbing Markov chains. We consider absorbing
   chains with r absorbing states, r>1, conditional on an eventual absorption
   into a specified state. The transition count for such a chain when suitably
   scaled is found to follow a multivariate normal distribution asymptotically.
THESAURUS:  Markov Processes; Random Processes
OTHER SUBJECTS:  Central Limit Theorem; Absorbing Markov Chains; Random
   Variables; Absorbing States; Multivariate Normal Distribution
CLASS CODES:  B0240Z; C1140Z
NOTES:  Treatment:  Theoretical/mathematical
   Abstract no.:  B9410-0240Z-006, C9410-1140Z-026
   Coden:  JIOSDC

Citation 2 --------------------------------------------------------------------
TITLE:         A functional central limit theorem for a nonequilibrium model of
                 interacting particles with unbounded intensity.
AUTHOR:        Bezandry, P.H. (Inst. de Recherche Math. Avancee, Univ. Louis
                 Pasteur, Strasbourg, France); Fernique, X.; Giroux, G.
PUBLICATION:   Journal of Statistical Physics (July 1993) vol.72, no.1-2, p.
                 329-53. (ISSN 0022-4715) 18 refs.
LOCATION:      Stanford
                 Physics Serials (Shelved alphabetically by title; Library has
                   c.1: 1, 1969-; c.2)
                 Chem & Chem Eng Serials (Shelved alphabetically by title;
                   Library has c.2: 1-3, 1969-71)
DOCUMENT TYPE: Journal article
LANGUAGE:      English
ABSTRACT:  Under suitable physically reasonable initial assumptions, a
   functional central limit theorem is obtained for a nonequilibrium model of
   randomly interacting particles with unbounded jump intensity. This model is
   related to a nonlinear Boltzmann-type equation.
THESAURUS:  Fluctuations; Markov Processes
OTHER SUBJECTS:  Functional Central Limit Theorem; Nonequilibrium Model;
   Interacting Particles with Unbounded Intensity; Randomly Interacting
   Particles; Unbounded Jump Intensity; Nonlinear Boltzmann-Type Equation;
   Markov Processes; Stochastic Processes; Fluctuations
CLASS CODES:  A0540
NOTES:  Treatment:  Theoretical/mathematical
   Abstract no.:  A9320-0540-004
   Coden:  JSTPBS

Citation 3 --------------------------------------------------------------------
TITLE:         A central limit theorem for autoregressive integrated moving
                 average processes.
AUTHOR:        Angus, J.E. (Dept. of Math., Claremont Grad. Sch., CA, USA)
PUBLICATION:   Mathematical and Computer Modelling (May 1993) vol.17, no.10, p.
                 3-9. (ISSN 0895-7177) 6 refs.
LOCATION:      Stanford
                 Math & Comp Sci Serials (Shelved alphabetically by title;
                   Library has c.1: 10, 1988-)
DOCUMENT TYPE: Journal article
LANGUAGE:      English
ABSTRACT:  A central limit theorem for normalized sums of random variables that
   form an autoregressive integrated moving average (ARIMA) process is
   developed. The need for such a limit theorem is discussed in connection with
   modeling total compensation costs associated with insurance or medical
   claims.
THESAURUS:  Statistical Analysis; Time Series
OTHER SUBJECTS:  Arima Processes; Central Limit Theorem; Autoregressive
   Integrated Moving Average Processes; Normalized Sums; Random Variables;
   Total Compensation Costs; Insurance; Medical Claims
CLASS CODES:  C1140Z
NOTES:  Treatment:  Theoretical/mathematical
   Abstract no.:  C9310-1140Z-007
   Coden:  MCMOEG

Citation 4 --------------------------------------------------------------------
TITLE:         A q-analog of the quantum central limit theorem for SU/sub
                 q/(2), q complex.
AUTHOR:        Lenczewski, H. (Hugo Steinhaus Center, Inst. of Mathe., Tech.
                 Univ., of Wroclaw, Poland)
PUBLICATION:   Journal of Mathematical Physics (Feb. 1993) vol.34, no.2, p.
                 480-9. (ISSN 0022-2488) 18 refs.
LOCATION:      Stanford
                 Physics Serials (Shelved alphabetically by title; Library has
                   c.1: 1, 1960-)
                 SLAC CENT. LAB. LIB. (Library has 1, 1960-)
DOCUMENT TYPE: Journal article
LANGUAGE:      English
ABSTRACT:  A q-analog of the central limit theorem for SU/sub q/(2), mod q mod
   not in (0,1) is studied. It is shown that in the q-quantum central limit
   sense SU/sub q/(2) converges to the algebra of the complex quantum
   q-oscillator.
THESAURUS:  Algebra; Harmonic Oscillators; Quantum Theory; Su/Sub 2/ Theory
OTHER SUBJECTS:  Q-Analog; Quantum Central Limit Theorem; Su/Sub Q/(2); Q
   Complex; Algebra; Complex Quantum Q-Oscillator
CLASS CODES:  A0365F; A0220; A0210; A0365G
NOTES:  Treatment:  Theoretical/mathematical
   Abstract no.:  A9310-0365-043
   Coden:  JMAPAQ

Citation 5 --------------------------------------------------------------------
TITLE:         On the central limit theorem for the multiple point range of
                 random walk.
AUTHOR:        Hamana, Y. (Dept. of Math., Tokyo Univ., Japan)
PUBLICATION:   Journal of the Faculty of Science, University of Tokyo, Section
                 1A (Mathematics) (25 Sept. 1992) vol.39, no.2, p. 339-63.
                 (ISSN 0040-8980) 8 refs.
LOCATION:      Stanford
               for Journal of mathematical sciences, the University of Tokyo.
                 Math & Comp Sci Serials (Shelved alphabetically by title;
                   Library has c.1: v.1(1994)-)
DOCUMENT TYPE: Journal article
LANGUAGE:      English
ABSTRACT:  Let R/sub n//sup (k)/ be the number of the lattice points entered by
   a random walk in a 5 or more dimensional integer lattice at least k times in
   the first n steps, where the random walk is defined by the sum of
   independent identically distributed random variables. The author proves the
   convergence of covariances, that is for each k, l>or=1, there exists lim/sub
   n to infinity / Cov(R/sub n//sup (k)/, R/sub n//sup (l)/)/n, and for a fixed
   integer K>or=1, the random vector (R/sub n//sup (1)/, R/sub n//sup (2)/, . .
   ., R/sub n//sup (K)/) obeys the central limit theorem.
THESAURUS:  Lattice Theory and Statistics; Random Processes
OTHER SUBJECTS:  Central Limit Theorem; Multiple Point Range; Random Walk;
   Convergence; Covariances
CLASS CODES:  A0540; A0550
NOTES:  Treatment:  Theoretical/mathematical
   Abstract no.:  A9304-0540-008
   Coden:  JFTMAT

Citation 6 --------------------------------------------------------------------
TITLE:         Rates of convergence in a central limit theorem for stochastic
                 processes defined by differential equations with a small
                 parameter.
AUTHOR:        Kouritzin, M.A. (Freiburg Univ., Germany); Heunis, A.J.
PUBLICATION:   Journal of Multivariate Analysis (Oct. 1992) vol.43, no.1, p.
                 58-109. (ISSN 0047-259X) 24 refs.
LOCATION:      Stanford
                 Math & Comp Sci Serials (Shelved alphabetically by title;
                   Library has c.1: 1, 1971-)
DOCUMENT TYPE: Journal article
LANGUAGE:      English
ABSTRACT:  Consider the random ordinary differential equation in R/sup d/ X/sup
   epsilon /( tau )=F(X/sup epsilon /( tau ), tau / epsilon ) subject to X/sup
   epsilon /(0)=x/sub 0/, where epsilon >0 and (F(x,t, omega ), t>or=0) is a
   stochastic process indexed by x in R/sup d/ which is regular to ensure that
   there is a unique solution X/sup epsilon /., omega ) on the interval 0<or=
   tau <or=1 for almost all omega . In a classical paper Khas'minskii (1966)
   shows, under broad regularity conditions covering many physical problems of
   interest, that one can associate with the above equation a certain nonrandom
   'averaged' ordinary differential equation x/sup 0/( tau )=F(x/sup 0/( tau ))
   subject to x/sup 0/(0)=x/sub 0/ such that (i) lim/sub e to 0/ sup/sub 0<or=
   tau <or=1/ E( mod X/sup epsilon /( tau )-x/sup 0/( tau ) mod )=0 and (ii) if
   Y/sup epsilon /( tau )= epsilon /sup -1/2/(X/sup epsilon /( tau )-x/sup 0/(
   tau )), then the family of process (Y/sup epsilon /( tau ), 0<or= tau <or=1)
   converges weakly to a certain limiting Gauss-Markov process (Y/sup 0/( tau
   ), 0<or= tau <or=1) as epsilon to 0. In this paper the authors establish a
   rate of convergence for the central limit theorem in (ii) under conditions
   only slightly more resistive than those required by Khas'minskii; in
   particular, (F(x,t, omega ), t>or=0) is allowed to be strong mixing and
   non-stationary.
THESAURUS:  Convergence; Differential Equations; Stochastic Processes
OTHER SUBJECTS:  Convergence Rates; Random Ordinary Differential Equation;
   Stochastic Process; Regularity Conditions; Gauss-Markov Process; Central
   Limit Theorem
CLASS CODES:  A0540; A0250; A0230
NOTES:  Treatment:  Theoretical/mathematical
   Abstract no.:  A9303-0540-002
   Coden:  JMVAAI

Citation 7 --------------------------------------------------------------------
TITLE:         An q-analog of the quantum central limit theorem for SU/sub
                 q/(2).
AUTHOR:        Lenczewski, R. (Hugo Steinhaus Center, Tech. Univ. of Wroclaw,
                 Poland); Podgorski, K.
PUBLICATION:   Journal of Mathematical Physics (Aug. 1992) vol.33, no.8, p.
                 2768-78. (ISSN 0022-2488) 26 refs.
LOCATION:      Stanford
                 Physics Serials (Shelved alphabetically by title; Library has
                   c.1: 1, 1960-)
                 SLAC CENT. LAB. LIB. (Library has 1, 1960-)
DOCUMENT TYPE: Journal article
LANGUAGE:      English
ABSTRACT:  A q-analog of the central limit theorem for SU/sub q/(2), q>0, is
   studied. It is shown that the limits of the moments and q-exponential
   generating functions for coherent states give for q>1 (0<q<1) the harmonic
   q-oscillator (q/sup -1/-oscillator) introduced by Biedenharn (1989) and
   Macfarlane (1989).
THESAURUS:  Harmonic Oscillators; Quantum Theory; Su/Sub 2/ Theory
OTHER SUBJECTS:  Quantum Central Limit Theorem; Su/Sub Q/(2); Q-Analog;
   Q-Exponential Generating Functions; Coherent States; Harmonic Q-Oscillator
CLASS CODES:  A0365F; A0220; A0365G
NOTES:  Treatment:  Theoretical/mathematical
   Abstract no.:  A9220-0365-006
   Coden:  JMAPAQ

Citation 8 --------------------------------------------------------------------
TITLE:         Central limit theorem for Burgers equation.
AUTHOR:        Griniv, O.O. (Moscow State Univ., Russia)
PUBLICATION:   Theoretical and Mathematical Physics (July 1991) vol.88, no.1,
                 p. 678-82. (ISSN 0040-5779)  Translation of:  Teoreticheskaya
                 i Matematicheskaya Fizika (July 1991) vol.88, no.1, p. 7-13.
                 (ISSN 0564-6162) 5 refs.
LOCATION:      Stanford
               for Theoretical and mathematical physics.
                 SLAC CENT. LAB. LIB. (Library has 1, 1969-)
                 Physics Serials (Shelved alphabetically by title; Library has
                   c.1: 1, 1969-)
               for Teoreticheskakila i matematicheskakila fizika.
                 Physics Serials (Shelved alphabetically by title; Library has
                   c.1: 1, 1969-)
DOCUMENT TYPE: Journal article
LANGUAGE:      English
ABSTRACT:  Suppose the potential of the initial field of the Cauchy problem of
   the Burgers equation is a homogeneous mean-square continuous Gaussian random
   field. The author shows that the correlation function of this field is
   summable absolutely or its square is summable. Then in the limit t to
   infinity the field of solutions of the original equation tends in its
   distribution to a Gaussian random vector field.
THESAURUS:  Wave Equations
OTHER SUBJECTS:  Central Limit Theorem; Burgers Equation; Cauchy Problem;
   Homogeneous Mean-Square Continuous Gaussian Random Field; Correlation
   Function; Gaussian Random Vector Field
CLASS CODES:  A0340K
NOTES:  Treatment:  Theoretical/mathematical
   Abstract no.:  A9211-0340K-006
   Coden:  TMFZAL

Citation 9 --------------------------------------------------------------------
TITLE:         Central limit theorem for a variance estimator of a diffusion
                 process in the plane.
AUTHOR:        Brugiere, P. (CEREMADE, Paris IX Univ., France)
PUBLICATION:   Comptes Rendus de l'Academie des Sciences, Serie I
                 (Mathematique) (19 Dec. 1991) vol.313, no.13, p. 943-6. (ISSN
                 0764-4442) 9 refs.
LOCATION:      Stanford
               for Comptes rendus de l'Acadbemie des sciences. Sberie I,
                   Mathbematique.
                 Lane Medical Periodicals (Library has v. 298-299 = 1984)
                 Math & Comp Sci Serials (Shelved alphabetically by title;
                   Library has c.4: 298, 1984-)
DOCUMENT TYPE: Journal article
LANGUAGE:      English
ABSTRACT:  The author proves a central limit theorem for a nonparametric
   estimator of the variance of a diffusion process in the plane. The proof
   uses the calculus of the moments of the estimator.
THESAURUS:  Diffusion; Statistical Analysis
OTHER SUBJECTS:  Variance Estimator; Diffusion Process; Central Limit Theorem;
   Nonparametric Estimator
CLASS CODES:  A0560; A0250
NOTES:  Treatment:  Theoretical/mathematical
   Abstract no.:  A9207-0560-001
   Coden:  CASMEI

Citation 10 -------------------------------------------------------------------
TITLE:         Central limit theorem for a variance estimator of a diffusion
                 process in the multidimensional case.
AUTHOR:        Brugiere, P. (Paris, Univ., France)
PUBLICATION:   Comptes Rendus de l'Academie des Sciences, Serie I
                 (Mathematique) (10 Oct. 1991) vol.313, no.8, p. 533-6. (ISSN
                 0764-4442) 8 refs.
LOCATION:      Stanford
               for Comptes rendus de l'Acadbemie des sciences. Sberie I,
                   Mathbematique.
                 Lane Medical Periodicals (Library has v. 298-299 = 1984)
                 Math & Comp Sci Serials (Shelved alphabetically by title;
                   Library has c.4: 298, 1984-)
DOCUMENT TYPE: Journal article
LANGUAGE:      French
ABSTRACT:  The author proves a central limit theorem for a nonparametric
   estimator of the variance of a diffusion process in the multidimensional
   case. The proof uses the calculus of the moments of the estimator.
THESAURUS:  Diffusion; Transport Processes; Variational Techniques
OTHER SUBJECTS:  Variance Estimator; Diffusion Process; Multidimensional Case;
   Central Limit Theorem; Nonparametric Estimator; Calculus; Moments
CLASS CODES:  A0560; A0230
NOTES:  Treatment:  Theoretical/mathematical
   Abstract no.:  A9202-0560-002
   Coden:  CASMEI

Citation 11 -------------------------------------------------------------------
TITLE:         Quantum q-white noise and a q-central limit theorem.
AUTHOR:        Schurmann, M. (Inst. fur Angewandte Math., Heidelberg Univ.,
                 Germany)
PUBLICATION:   Communications in Mathematical Physics (1991) vol.140, no.3, p.
                 589-615. (ISSN 0010-3616) 41 refs.
LOCATION:      Stanford
                 SLAC CENT. LAB. LIB. (Library has 1, 1965-)
                 Physics (Shelved alphabetically by title; SERIALS COLL;
                   Library has 1, 1965-)
DOCUMENT TYPE: Journal article
LANGUAGE:      English
ABSTRACT:  The author establishes a connection between the Azema martingales
   (1985) and certain quantum stochastic processes with increments satisfying
   q-commutation relations. This leads to a theory of q-white noise on
   q-*-bialgebras and to a generalization of the Fock space representation
   theorem for white noise on *-bialgebras. In particular, quantum Azema noise,
   q-interpolations between fermion and boson quantum Brownian motion and
   unitary evolutions with q-independent multiplicative increments are studied.
   It follows from his results that the Azema martingales and the
   q-interpolations are central limits of sums of q-independent, identically
   distributed quantum random variables.
THESAURUS:  Quantum Statistical Mechanics; Stochastic Processes; White Noise
OTHER SUBJECTS:  Azema Martingales; Quantum Stochastic Processes; Q-Commutation
   Relations; Q-White Noise; Fock Space Representation Theorem; Quantum Azema
   Noise; Quantum Brownian Motion; Q-Independent Multiplicative Increments;
   Quantum Random Variables
CLASS CODES:  A0530; A0540
NOTES:  Treatment:  Theoretical/mathematical
   Abstract no.:  A9202-0530-001
   Coden:  CMPHAY

Citation 12 -------------------------------------------------------------------
TITLE:         A central limit theorem in nonlinear filtering.
AUTHOR:        Mayer-Wolf, E. (Dept. of Math., Technion-Israel Inst. of
                 Technol., Haifa, Israel)
PUBLICATION:   Stochastics and Stochastics Reports (1991) vol.35, no.4, p.
                 191-211. (ISSN 1045-1129) 22 refs.
LOCATION:      Stanford
                 Stanford Auxiliary Library QA274.A1 S78 (Library has c.1:
                   [34-37, 1991])
DOCUMENT TYPE: Journal article
LANGUAGE:      English
ABSTRACT:  It is shown that the probability law of a diffusion process
   conditioned on weakly corrupted observations is asymptotically Gaussian when
   properly scaled. The method of proof involves Fisher information matrices
   and a Cramer-Rao inequality.
THESAURUS:  Diffusion; Filtering and Prediction Theory; Probability
OTHER SUBJECTS:  Asymptotically Gaussian Probability Low; Central Limit
   Theorem; Nonlinear Filtering; Diffusion Process; Weakly Corrupted
   Observations; Fisher Information Matrices; Cramer-Rao Inequality
CLASS CODES:  C1260; C1140Z
NOTES:  Treatment:  Theoretical/mathematical
   Abstract no.:  C9201-1260-007
   Coden:  SSTREY

Citation 13 -------------------------------------------------------------------
TITLE:         Central limit theorem for density estimator and integrated
                 square error based on nonstationary random variables.
AUTHOR:        Harel, M.; Puri, M.
PUBLICATION:   Comptes Rendus de l'Academie des Sciences, Serie I
                 (Mathematique) (3 Jan. 1991) vol.312, no.1, p. 145-8. (ISSN
                 0764-4442) 6 refs.
LOCATION:      Stanford
               for Comptes rendus de l'Acadbemie des sciences. Sberie I,
                   Mathbematique.
                 Lane Medical Periodicals (Library has v. 298-299 = 1984)
                 Math & Comp Sci Serials (Shelved alphabetically by title;
                   Library has c.4: 298, 1984-)
DOCUMENT TYPE: Journal article
LANGUAGE:      English
ABSTRACT:  The central limit theorems for the density estimator and for the
   integrated square error are proved for the case when the underlying sequence
   of random variables is nonstationary. Applications to Markov processes and
   ARMA processes are provided.
THESAURUS:  Error Analysis; Markov Processes; Probability; Random Processes
OTHER SUBJECTS:  Density Estimator; Integrated Square Error; Nonstationary
   Random Variables; Central Limit Theorems; Markov Processes; Arma Processes
CLASS CODES:  A0540; A0250
NOTES:  Treatment:  Theoretical/mathematical
   Abstract no.:  A91051803
   Coden:  CASMEI

Citation 14 -------------------------------------------------------------------
TITLE:         Rates in the central limit theorem for mixing random fields
                 satisfying low moment assumptions.
AUTHOR:        Bulinskii, A.V. (Moscow Univ., USSR); Doukhan, P.
PUBLICATION:   Comptes Rendus de l'Academie des Sciences, Serie I
                 (Mathematique) (6 Dec. 1990) vol.311, no.12, p. 801-5. (ISSN
                 0764-4442) 20 refs.
LOCATION:      Stanford
               for Comptes rendus de l'Acadbemie des sciences. Sberie I,
                   Mathbematique.
                 Lane Medical Periodicals (Library has v. 298-299 = 1984)
                 Math & Comp Sci Serials (Shelved alphabetically by title;
                   Library has c.4: 298, 1984-)
DOCUMENT TYPE: Journal article
LANGUAGE:      English
ABSTRACT:  The authors give an expression for the rate of convergence in the
   central limit theorem for mixing random fields assuming low moment
   assumptions, e.g. EX/sup 2/ln/sup delta //sub +/(X)< infinity . They use,
   for it, a truncation in Bulinskii's (1986) results leading to results
   analogous to those well known in the independent case.
THESAURUS:  Convergence; Random Processes
OTHER SUBJECTS:  Convergence Rate; Central Limit Theorem; Mixing Random Fields;
   Low Moment
CLASS CODES:  A0540; A0250
NOTES:  Treatment:  Theoretical/mathematical
   Abstract no.:  A91032464
   Coden:  CASMEI

Citation 15 -------------------------------------------------------------------
TITLE:         Intermittency and the central limit theorem.
AUTHOR:        Alberty, J.M. (CERN, Geneva, Switzerland); Bialas, A.
PUBLICATION:   Zeitschrift fur Physik C (Particles and Fields) (1991) vol.50,
                 no.2, p. 315-20. (ISSN 0170-9739) 15 refs.
LOCATION:      Stanford
               for Zeitschrift fhur Physik. C: Particles and fields.
                 SLAC CENT.LAB.LIB. (Library has 1, 1979-)
                 Physics Serials (Shelved alphabetically by title; Library has
                   c.1: 1, 1979-)
DOCUMENT TYPE: Journal article
LANGUAGE:      English
ABSTRACT:  Central limit theorem estimates of anomalous fractal dimensions of
   self-similar random cascades are studied. It is found that, in general, the
   normal approximation fails badly. A systematic series of approximations
   which converges to the exact result (both for the fractal dimensions and for
   the distribution itself) is derived for the alpha -model. Consequences for
   the 'empty bin effect' are indicated.
THESAURUS:  Fractals; Statistical Models
OTHER SUBJECTS:  Alpha-Model; Intermittency; Central Limit Theorem; Anomalous
   Fractal Dimensions; Self-Similar Random Cascades; Empty Bin Effect
CLASS CODES:  A1240E
NOTES:  Treatment:  Theoretical/mathematical
   Abstract no.:  A91084165
   Coden:  ZPCFD2

Citation 16 -------------------------------------------------------------------
TITLE:         Globally coupled chaos violates the law of large numbers but not
                 the central-limit theorem.
AUTHOR:        Kaneko, K. (Inst. of Phys., Coll. of Arts. & Sci., Tokyo Univ.,
                 Japan)
PUBLICATION:   Physical Review Letters (17 Sept. 1990) vol.65, no.12, p.
                 1391-4. (ISSN 0031-9007) 12 refs.
LOCATION:      Stanford
                 Lane Medical Compact Shelving (Library has v. 1, [2], 3-7,
                   [8], 9, [10], 11, [12-13, 16, 18, 22-23, 31] = 1958, [1959],
                   1960-61, [1962-64, 1966-67, 1969, 1973].)
                 Applied Physics Dept Serials (Shelved alphabetically by title;
                   Library has c.2: 1-35, 1958-75; 44-53, 1980-84;[54-55,
                   1985]; c.4: 1-65, 1958-90)
                 Physics Serials (Shelved alphabetically by title; Library has
                   c.1: 1, 1958-)
                 Stanford Auxiliary Library 530.5.P56 (Library has c.3: 1-43,
                   1959-79)
                 Chem & Chem Eng Serials (Shelved alphabetically by title;
                   Library has c.7: 4, 1960-)
DOCUMENT TYPE: Journal article
LANGUAGE:      English
ABSTRACT:  The title statement is numerically shown for a globally coupled
   chaotic system. With an increasing number of elements N, the distribution of
   the mean field approaches a Gaussian distribution, but the decrease of its
   mean-square deviation with N stops for large N. This violation of the law of
   large numbers is found to be caused by the emergence of a subtle coherence
   among elements, as is measured by the mutual information. With the inclusion
   of noise, the law of large numbers is restored. The mean-square deviation
   decreases in proportion to N/sup - beta / with an exponent beta <1 depending
   on the noise strength.
THESAURUS:  Chaos
OTHER SUBJECTS:  Chaos; Law of Large Numbers; Central-Limit Theorem; Globally
   Coupled Chaotic System; Mean Field; Gaussian Distribution; Mean-Square
   Deviation; Noise
CLASS CODES:  A0545
NOTES:  Treatment:  Theoretical/mathematical
   Abstract no.:  A90143522
   Coden:  PRLTAO

Citation 17 -------------------------------------------------------------------
TITLE:         A law of large numbers and a central limit theorem for disk
                 polynomial Markov chains on N/sup 2/.
AUTHOR:        Bouhaik, M.; Gallardo, L.
PUBLICATION:   Comptes Rendus de l'Academie des Sciences, Serie I
                 (Mathematique) (10 May 1990) vol.310, no.10, p. 739-44. (ISSN
                 0764-4442) 8 refs.
LOCATION:      Stanford
               for Comptes rendus de l'Acadbemie des sciences. Sberie I,
                   Mathbematique.
                 Lane Medical Periodicals (Library has v. 298-299 = 1984)
                 Math & Comp Sci Serials (Shelved alphabetically by title;
                   Library has c.4: 298, 1984-)
DOCUMENT TYPE: Journal article
LANGUAGE:      English
ABSTRACT:  The authors describe the asymptotic behaviour of a class of Markov
   chains on N/sup 2/ associated with the disk polynomial hypergroup. This
   shows some nonclassical probability measures on R/sub +/ and R/sub +/*R/sub
   +/.
THESAURUS:  Group Theory; Markov Processes; Polynomials
OTHER SUBJECTS:  Large Numbers; Central Limit Theorem; Disk Polynomial Markov
   Chains; N/Sup 2/; Asymptotic Behaviour; Disk Polynomial Hypergroup;
   Nonclassical Probability Measures
CLASS CODES:  A0540; A0250; A0210; A0220
NOTES:  Treatment:  Theoretical/mathematical
   Abstract no.:  A90092989
   Coden:  CASMEI

Citation 18 -------------------------------------------------------------------
TITLE:         Asymmetry and convergence in the central limit theorem: an
                 approach for physicists.
AUTHOR:        Pury, P.A. (Fac. de Matematica, Astron. y Fisica, Univ. Nacional
                 de Cordoba, Argentina)
PUBLICATION:   American Journal of Physics (Jan. 1990) vol.58, no.1, p. 62-7.
                 (ISSN 0002-9505) 6 refs.
LOCATION:      Stanford
                 SLAC CENT. LAB. LIB.
                 Applied Physics Dept Serials (Shelved alphabetically by title;
                   Library has c.2: 38-58, 1970-90)
                 Physics Serials (Shelved alphabetically by title; Library has
                   c.1: 1, 1933-)
DOCUMENT TYPE: Journal article
LANGUAGE:      English
ABSTRACT:  A version of the central limit theorem is presented that allows the
   study of the rate of convergence to the normal probability density of the
   average of independent identically distributed random variables. Particular
   emphasis is put on the effect due to the asymmetry of the probability
   density of the variables. An example is worked out that gives a convincing
   visual display of the theorem and its convergence.
THESAURUS:  Random Processes; Teaching
OTHER SUBJECTS:  Central Limit Theorem; Probability Density; Identically
   Distributed Random Variables; Asymmetry; Convergence
CLASS CODES:  A0150K; A0540
NOTES:  Treatment:  Theoretical/mathematical
   Abstract no.:  A90050695
   Coden:  AJPIAS

Citation 19 -------------------------------------------------------------------
TITLE:         A central limit theorem for decomposable random variables with
                 applications to random graphs.
AUTHOR:        Barbour, A.D. (Inst. fur Angewandte Math., Zurich Univ.,
                 Switzerland); Karonski, M.; Rucinski, A.
PUBLICATION:   Journal of Combinatorial Theory, Series B (Oct. 1989) vol.47,
                 no.2, p. 125-45. (ISSN 0095-8956) 24 refs.
LOCATION:      Stanford
                 Engineering Serials (Shelved alphabetically by title; Library
                   has c.1: 10-43, 1971-87)
                 Math & Comp Sci Serials (Shelved alphabetically by title;
                   Library has c.2: 10, 1971-)
DOCUMENT TYPE: Journal article
LANGUAGE:      English
ABSTRACT:  The application of Stein's method of obtaining rates of convergence
   to the normal distribution is illustrated in the context of random graph
   theory. Problems which exhibit a dissociated structure and problems which do
   not are considered. Results are obtained for the number of copies of a given
   graph G in K(n, p), for the number of induced copies of G, for the number of
   isolated trees of order k>or=2, for the number of vertices of degree d>or=1,
   and for the number of isolated vertices.
THESAURUS:  Graph Theory
OTHER SUBJECTS:  Central Limit Theorem; Decomposable Random Variables; Random
   Graphs; Stein's Method; Rates of Convergence; Trees; Isolated Vertices
CLASS CODES:  B0250; C1160
NOTES:  Treatment:  Theoretical/mathematical
   Abstract no.:  B90013612, C90010629
   Coden:  JCBTB8

Citation 20 -------------------------------------------------------------------
TITLE:         Central limit theorem for semi-Markov random evolutions.
AUTHOR:        Koroljuk, V.S. (Math. Inst., Acad. of Sci., Kiev, Ukrainian SSR,
                 USSR)
PUBLICATION:   Computers & Mathematics with Applications (1990) vol.19, no.1,
                 p. 83-8. (ISSN 0097-4943) 7 refs.
LOCATION:      Stanford
                 Math & Comp Sci Serials (Shelved alphabetically by title;
                   Library has c.1: 1-11, 1975-85//)
               for Computers & mathematics with applications (Oxford,
                   Oxfordshire : 1987). Computers & mathematics with
                   applications.
                 Math & Comp Sci Serials (Shelved alphabetically by title;
                   Library has c.1: 13, 1987-)
               for Computers & mathematics with applications. Part A.
                 Math & Comp Sci Serials (Shelved alphabetically by title;
                   Library has c.1: 12, 1986//)
DOCUMENT TYPE: Journal article
LANGUAGE:      English
ABSTRACT:  A new type of central limit theorems for random evolutions with
   semi-Markov switch-overs in a scheme of series is discussed. The
   applications to switching processes, storage and traffic processes are also
   considered.
THESAURUS:  Markov Processes; Stochastic Systems
OTHER SUBJECTS:  Central Limit Theorems; Random Evolutions; Semi-Markov
   Switch-Overs; Switching Processes; Traffic Processes
CLASS CODES:  C1140Z
NOTES:  Treatment:  Theoretical/mathematical
   Abstract no.:  C90010542
   Coden:  CMAPDK

Citation 21 -------------------------------------------------------------------
TITLE:         Thermodynamic limit and central limit theorem for point random
                 fields in non-ergodic case.
AUTHOR:        Parczyk, K. (Inst. of Math., Nicholas Copernicus Univ., Torun,
                 Poland); Maslowski, T.
PUBLICATION:   Reports on Mathematical Physics (Aug. 1988) vol.26, no.1, p.
                 1-15. (ISSN 0034-4877) 43 refs.
LOCATION:      Stanford
                 SLAC CENT.LAB.LIB (Library has 1-24, 1970-86)
                 Physics Serials (Shelved alphabetically by title; Library has
                   c.1: 1, 1970-)
DOCUMENT TYPE: Journal article
LANGUAGE:      English
ABSTRACT:  The central limit theorem for a class of point random fields,
   including also nonergodic measures, is proven. The result, mathematically
   easy, shows the differences in quality between point random fields
   (continuous case) and random fields (discrete case).
THESAURUS:  Random Processes; Thermodynamics
OTHER SUBJECTS:  Central Limit Theorem; Point Random Fields; Nonergodic
   Measures
CLASS CODES:  A0570J; A0540
NOTES:  Treatment:  Theoretical/mathematical
   Abstract no.:  A89090746
   Coden:  RMHPBE

Citation 22 -------------------------------------------------------------------
TITLE:         Central limit theorem for mixing quantum systems and the
                 CCR-algebra of fluctuations.
AUTHOR:        Goderis, D. (Inst. voor Theor. Fysica, Leuven Univ., Belgium);
                 Vets, P.
PUBLICATION:   Communications in Mathematical Physics (1989) vol.122, no.2, p.
                 249-65. (ISSN 0010-3616) 20 refs.
LOCATION:      Stanford
                 SLAC CENT. LAB. LIB. (Library has 1, 1965-)
                 Physics (Shelved alphabetically by title; SERIALS COLL;
                   Library has 1, 1965-)
DOCUMENT TYPE: Journal article
LANGUAGE:      English
ABSTRACT:  The authors analyse macroscopic fluctuations of an infinite quantum
   system and introduce the CCR-C*-algebra of normal fluctuations. A
   non-commutative central limit theorem for mixing quantum systems is proved.
THESAURUS:  Algebra; Fluctuations; Lattice Theory and Statistics; Quantum
   Statistical Mechanics; Quantum Theory
OTHER SUBJECTS:  Lattice Theory; Fluctuations; Infinite Quantum System;
   Ccr-C*-Algebra; Central Limit Theorem
CLASS CODES:  A0530; A0540; A0210; A0550; A0365F
NOTES:  Treatment:  Theoretical/mathematical
   Abstract no.:  A89090653
   Coden:  CMPHAY

Citation 23 -------------------------------------------------------------------
TITLE:         An almost everywhere central limit theorem for the occupation
                 measures of Brownian motion on a compact Riemannian manifold.
AUTHOR:        Brosamler, G.A. (Univ. des Saarlandes, Saarbrucken, West
                 Germany)
PUBLICATION:   Comptes Rendus de l'Academie des Sciences, Serie I
                 (Mathematique) (7 Dec. 1988) vol.307, no.18, p. 919-22. (ISSN
                 0249-6291) 3 refs.
LOCATION:      Stanford
               for Comptes rendus des sbeances de l'Acadbemie des sciences.
                   Sberie I, Mathbematique.
                 Lane Medical Periodicals (Library has v. [292-293], 294,
                   [295], 296-297 = [1981-82], 1983)
                 Math & Comp Sci Serials (Shelved alphabetically by title;
                   Library has c.4: 292-297, 1981-83//)
                 Math & Comp Sci
DOCUMENT TYPE: Journal article
LANGUAGE:      English
ABSTRACT:  The author gives an almost everywhere central limit theorem for
   Brownian motion on a compact Riemannian manifold. This theorem allows one to
   obtain the spectrum of the Laplacian by observing the energy of a trajectory
   for large times.
THESAURUS:  Brownian Motion; Geometry
OTHER SUBJECTS:  Almost Everywhere Central Limit Theorem; Occupation Measures;
   Brownian Motion; Compact Riemannian Manifold; Laplacian
CLASS CODES:  A0540; A0240
NOTES:  Treatment:  Theoretical/mathematical
   Abstract no.:  A89045550
   Coden:  CASMEI

Citation 24 -------------------------------------------------------------------
TITLE:         Sharp orders of convergence in the random central limit theorem.
AUTHOR:        Landers, D. (Math. Inst., Koln Univ., West Germany); Rogge, L.
PUBLICATION:   Journal of Approximation Theory (April 1988) vol.53, no.1, p.
                 86-111. (ISSN 0021-9045) 25 refs.
LOCATION:      Stanford
                 Math & Comp Sci Serials (Shelved alphabetically by title;
                   Library has c.1: 1, 1968-)
DOCUMENT TYPE: Journal article
LANGUAGE:      English
ABSTRACT:  The authors discuss the rates of convergence for the classical
   random central limit theorem H/sub n/( tau ). The paper closes the wide gap
   between constant and non-constant limit functions tau .
THESAURUS:  Approximation Theory
OTHER SUBJECTS:  Sharp Orders of Convergence; Approximation Theory; Orders of
   Convergence; Random Central Limit Theorem
CLASS CODES:  B0290F; C4130
NOTES:  Treatment:  Theoretical/mathematical
   Abstract no.:  B89000468, C89001558
   Coden:  JAXTAZ

Citation 25 -------------------------------------------------------------------
TITLE:         The rate of convergence in the central limit theorem for
                 non-stationary dependent random vectors.
AUTHOR:        Glendinning, R. (Birkbeck Coll., London Univ., UK)
PUBLICATION:   Journal of Multivariate Analysis (July 1988) vol.26, no.1, p.
                 89-103. (ISSN 0047-259X) 15 refs.
LOCATION:      Stanford
                 Math & Comp Sci Serials (Shelved alphabetically by title;
                   Library has c.1: 1, 1971-)
DOCUMENT TYPE: Journal article
LANGUAGE:      English
ABSTRACT:  Let (X/sub j/,j>or=1) be a strictly stationary sequence of uniformly
   mixing random variables with zero mean, unit variance and finite fourth
   moment. Form the vector S/sub n/= Sigma /sub j=1//sup n/ alpha /sub nj/X/sub
   j/ where alpha /sub nj/=( alpha /sub nj1/, alpha /sub nj2/)/sup t/, alpha
   /sub nj1/, alpha /sub nj2/ in R/sup 1/ and mod alpha /sub nj1/ mod <or=1,
   mod alpha /sub nj2/ mod <or=1. The author estimates the rate at which S/sub
   n/ converges to normality. The extension of this result to bounded R/sup
   s/-valued weights (s>or=1) is immediate.
THESAURUS:  Convergence; Random Processes; Vectors
OTHER SUBJECTS:  Convergence Rate; Nonstationary Dependent Random Vectors;
   Central Limit Theorem; Uniformly Mixing Random Variables; Bounded R/Sup
   S/-Valued Weights
CLASS CODES:  A0210; A0540
NOTES:  Treatment:  Theoretical/mathematical
   Abstract no.:  A88131961
   Coden:  JMVAAI

Citation 26 -------------------------------------------------------------------
TITLE:         A law of large numbers and a central limit theorem for the
                 Schrodinger operator with zero-range potentials.
AUTHOR:        Figari, R. (Res. Center Bielefeld-Bochum-Stochastics, West
                 Germany); Holden, H.; Teta, A.
PUBLICATION:   Journal of Statistical Physics (April 1988) vol.51, no.1-2, p.
                 205-14. (ISSN 0022-4715) 10 refs.
LOCATION:      Stanford
                 Physics Serials (Shelved alphabetically by title; Library has
                   c.1: 1, 1969-; c.2)
                 Chem & Chem Eng Serials (Shelved alphabetically by title;
                   Library has c.2: 1-3, 1969-71)
DOCUMENT TYPE: Journal article
LANGUAGE:      English
ABSTRACT:  The authors consider the Schrodinger operator with zero-range
   potentials on N points of three-dimensional space, independently chosen
   according to a common distribution V(x). Under some assumptions they prove
   that, when N goes to infinity, the sequence converges to a Schrodinger
   operator with an effective potential. The fluctuations around the limit
   operator are explicitly characterized.
THESAURUS:  Fluctuations; Quantum Theory; Schrodinger Equation
OTHER SUBJECTS:  Large Numbers Law; Central Limit Theorem; Schrodinger
   Operator; Zero-Range Potentials; Effective Potential; Fluctuations; Limit
   Operator
CLASS CODES:  A0365G
NOTES:  Treatment:  Theoretical/mathematical
   Abstract no.:  A88115160
   Coden:  JSTPBS

Citation 27 -------------------------------------------------------------------
TITLE:         Comprehending the Central Limit Theorem.
AUTHOR:        Kerley, L.M. (Dept. of Math., East Tennessee State Univ.,
                 Johnson City, TN, USA)
PUBLICATION:   SIGCSE Bulletin (June 1988) vol.20, no.2, p. 20-5. (ISSN
                 0097-8418) 7 refs.
LOCATION:      Stanford
               for Association for Computing Machinery. Special Interest Group
                   on Computer Science Education. SIGCSE bulletin.
                 Math & Comp Sci Serials (Shelved alphabetically by title;
                   Library has c.1: 2, 1970-)
DOCUMENT TYPE: Journal article
LANGUAGE:      English
ABSTRACT:  Simulation is used to illustrate the Central Limit Theorem and the
   concept of testing a hypothesis. The outline of a Pascal program for
   generating various statistical distributions and testing the Central Limit
   Theorem, is presented.
THESAURUS:  Digital Simulation; Mathematics Computing; Pascal Listings;
   Statistical Analysis
OTHER SUBJECTS:  Hypothesis Testing; Simulation; Central Limit Theorem; Pascal
   Program; Statistical Distributions
CLASS CODES:  C7310
NOTES:  Treatment:  Practical
   Abstract no.:  C88053345
   Coden:  SIGSD3

Citation 28 -------------------------------------------------------------------
TITLE:         Some pairwise independent sequences for which the central limit
                 theorem fails.
AUTHOR:        Janson, S. (Dept. of Math., Uppsala Univ., Sweden)
PUBLICATION:   Stochastics (1988) vol.23, no.4, p. 439-48. (ISSN 0090-9491) 4
                 refs.
LOCATION:      Stanford
                 Engineering Serials (Shelved alphabetically by title; Library
                   has c.2: 3-4, 1979-80; [5, 1981]; 6-15, 1981/82-85)
                 Stanford Auxiliary Library QA274.A1 S78 (Library has c.1: [1,
                   1974/75]; 2-15, 1976/79-85)
               for Stochastics and stochastics reports.
                 Stanford Auxiliary Library QA274.A1 S78 (Library has c.1:
                   [34-37, 1991])
DOCUMENT TYPE: Journal article
LANGUAGE:      English
ABSTRACT:  Some simple examples are given of stationary, pairwise independent
   sequences of random variables for which the central limit theorem utterly
   fails.
THESAURUS:  Probability
OTHER SUBJECTS:  Probability; Pairwise Independent Sequences; Central Limit
   Theorem; Random Variables
CLASS CODES:  C1140Z
NOTES:  Treatment:  Theoretical/mathematical
   Abstract no.:  C88043324
   Coden:  STOCB2

Citation 29 -------------------------------------------------------------------
TITLE:         Anomalous diffusion in disordered media: trapping, correlations
                 and the central limit theorem.
AUTHOR:        Bouchaud, J.-P. (Lab. de Spectroscopie Hertzienne de l'Ecole
                 Normale Superieure, Paris, France); Georges, A.; Le Doussal,
                 P.
PUBLICATION:   Journal de Physique (Nov. 1987) vol.48, no.11, p. 1855-60. (ISSN
                 0302-0738) 20 refs.
LOCATION:      Stanford
                 Physics Serials (Shelved alphabetically by title; Library has
                   c.1: ser.1:1-10, 1872-81; ser.2:1-10, 1882-91;; ser.3:1-10,
                   1892-1901; ser.4:1-9, 1902-10;; ser.5:[1-9, 1911-19];
                   ser.6:1-10, 1920-29;; ser.7:1-10, 1930-39; ser.8:1-51,
                   1940-90)
DOCUMENT TYPE: Journal article
LANGUAGE:      French
ABSTRACT:  Simple physical arguments are developed, allowing to predict the
   asymptotic behaviour of random walks in random media. It is shown that
   anomalous diffusion originates from distributions (for example of effective
   trapping times) with long tails, or from long-range correlations. This leads
   either to subdiffusive or superdiffusive behaviours.
THESAURUS:  Diffusion; Lattice Theory and Statistics; Random Processes
OTHER SUBJECTS:  Central Limit Theorem; Asymptotic Behaviour; Random Walks;
   Random Media; Anomalous Diffusion; Effective Trapping Times; Long Tails;
   Long-Range Correlations; Subdiffusive; Superdiffusive
CLASS CODES:  A0540; A0550; A0560
NOTES:  Treatment:  Theoretical/mathematical
   Abstract no.:  A88024343
   Coden:  JOPQAG

Citation 30 -------------------------------------------------------------------
TITLE:         A central limit theorem for fuzzy random variables.
AUTHOR:        Boswell, S.B. (Dept. of Biostat., Harvard Univ. Sch. of Public
                 Health, Boston, MA, USA); Taylor, M.S.
PUBLICATION:   Fuzzy Sets and Systems (Dec. 1987) vol.24, no.3, p. 331-44.
                 (ISSN 0165-0114) 20 refs.
LOCATION:      Stanford
                 Publication not found in Socrates.  Type HELP LOCATION.
DOCUMENT TYPE: Journal article
LANGUAGE:      English
ABSTRACT:  Fuzzy random variables have been proposed to treat situations in
   which both random behavior and fuzzy perception must be considered. A
   definition of independence is given for fuzzy random variables, as well as a
   notion of fuzzy Gaussian random variables. It is shown that a sum or mean of
   independent fuzzy random variables converges in the limit to a fuzzy
   Gaussian random variable, thus providing a fuzzy analogue of the central
   limit theorem of classical probability theory.
THESAURUS:  Fuzzy Set Theory; Probability; Random Processes
OTHER SUBJECTS:  Central Limit Theorem; Fuzzy Random Variables; Fuzzy
   Perception; Definition; Fuzzy Gaussian Random Variables; Probability Theory
CLASS CODES:  C1140Z; C1160
NOTES:  Treatment:  Theoretical/mathematical
   Abstract no.:  C88010304
   Coden:  FSSYD8

Citation 31 -------------------------------------------------------------------
TITLE:         Entropy and the central limit theorem in quantum mechanics.
AUTHOR:        Streater, R.F. (Dept. of Math., King's Coll., London, UK)
PUBLICATION:   Journal of Physics A (Mathematical and General) (11 Sept. 1987)
                 vol.20, no.13, p. 4321-30. (ISSN 0305-4470) 32 refs.
LOCATION:      Stanford
                 Applied Physics Dept Serials (Shelved alphabetically by title;
                   Library has c.2: 8-16, 1975-83; [17, 1984]; 18-21, 1985-88)
                 Physics Serials (Shelved alphabetically by title; Library has
                   c.1: 8, 1975-)
                 SLAC CENT. LAB. LIB. (Library has 10, 1977-)
DOCUMENT TYPE: Journal article
LANGUAGE:      English
ABSTRACT:  Gives a short proof that any infinitely divisible even
   representation of a Clifford algebra or a CAR algebra is quasi-free, and of
   Hudson's central limit theorem (1973) for fermions. The author shows that
   the entropy of any even state of the CAR, Clifford or CCR algebra is less
   than or equal to the entropy of the quasi-free state with the same two-point
   function.
THESAURUS:  Algebra; Entropy; Quantum Theory
OTHER SUBJECTS:  Clifford Algebra; Car Algebra; Central Limit Theorem;
   Fermions; Entropy; Ccr Algebra; Quasi-Free State; Two-Point Function
CLASS CODES:  A0210; A0365B
NOTES:  Treatment:  Theoretical/mathematical
   Abstract no.:  A88004715
   Coden:  JPHAC5

