Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Volume 2: Contributions to Probability Theory

Fourth Berkeley Symposium on Mathematical Statistics and Probability

June 20-July 30, 1960 | Statistical Laboratory of the University of California, Berkeley

Editor(s) Jerzy Neyman

Berkeley Symp. on Math. Statist. and Prob., 4.2: 633pp. (1961).

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Berkeley Symposium on Mathematical Statistics and Probability, Volume 4.2

633 pp.

Published: 1961

First available in Project Euclid: 17 January 2008

Keywords: Mathematical statistics--Congresses , Probabilities

Berkeley Symposium on Mathematical Statistics and Probability

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University of California Press

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Miscellaneous front pages, Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Vol. 2: Contributions to Probability Theory

Berkeley Symposium on Mathematical Statistics and Probability Vol. 4.2, - (1961). Open Access

Alexander Iacovlevich Khinchin

B. V. Gnedenko

Berkeley Symposium on Mathematical Statistics and Probability Vol. 4.2, 1-15 (1961). Open Access

KEYWORDS: Obituary, 01.50

Appreciation of Khinchin

J. L. Doob

Berkeley Symposium on Mathematical Statistics and Probability Vol. 4.2, 17-20 (1961). Open Access

KEYWORDS: Biography, 85.00, 85.60

Continuity and Hölder's Conditions for Sample Functions of Stationary Gaussian Processes

Yu. K. Belayev

Berkeley Symposium on Mathematical Statistics and Probability Vol. 4.2, 23-33 (1961). Open Access

KEYWORDS: Correlation function, Local properties of sample functions

Probabilistic Methods in Markov Chains

K. L. Chung

Berkeley Symposium on Mathematical Statistics and Probability Vol. 4.2, 35-56 (1961). Open Access

KEYWORDS: Continuous time, Transition intensity, Entrance problem, Fictitious state, 60.65

On Some Classes of Nonstationary Stochastic Processes

Harald Cramér

Berkeley Symposium on Mathematical Statistics and Probability Vol. 4.2, 57-78 (1961). Open Access

KEYWORDS: Spectral representation, Finite second-order moment, Normal shift operator, 60.40

A Stochastic Treatment of Some Classical Interpolation Problems

J. H. Curtiss

Berkeley Symposium on Mathematical Statistics and Probability Vol. 4.2, 79-93 (1961). Open Access

KEYWORDS: Trigonometric interpolation, Jordan curve, Complex domain, Uniform convergence, 41.10

Notes on Martingale Theory

J. L. Doob

Berkeley Symposium on Mathematical Statistics and Probability Vol. 4.2, 95-102 (1961). Open Access

KEYWORDS: Submartingale convergence, Potential theory, Upcrossing inequality, Green space, 60.40

Nonincrease Everywhere of the Brownian Motion Process

A. Dvoretzky , P. Erd?s , S. Kakutani

Berkeley Symposium on Mathematical Statistics and Probability Vol. 4.2, 103-116 (1961). Open Access

KEYWORDS: 60.62

Transformations of Markov Processes Connected with Additive Functionals

E. B. Dynkin

Berkeley Symposium on Mathematical Statistics and Probability Vol. 4.2, 117-142 (1961). Open Access

KEYWORDS: Transition function, Multiplicative functional, 60.60

Characterization of Sample Functions of Stochastic Processes by Some Absolute Probabilities

Marek Fisz

Berkeley Symposium on Mathematical Statistics and Probability Vol. 4.2, 143-151 (1961). Open Access

KEYWORDS: Jump function, Martingale, 60.40

Asymptotic Expansions in Probability Theory

B. V. Gnedenko , V. S. Koroluk , A. V. Skorokhod

Berkeley Symposium on Mathematical Statistics and Probability Vol. 4.2, 153-170 (1961). Open Access

KEYWORDS: Boundaries of random walk, Rate of convergence, 60.30

Stochastic Groups and Related Structures

Ulf Grenander

Berkeley Symposium on Mathematical Statistics and Probability Vol. 4.2, 171-184 (1961). Open Access

KEYWORDS: Linear vector space, Banach algebra, Topological groups, 60.08

Random Operator Equations

Otto Hanš

Berkeley Symposium on Mathematical Statistics and Probability Vol. 4.2, 185-202 (1961). Open Access

KEYWORDS: Contraction mapping, Linear bounded operator, Experience theory, Random integral equation, Stochastic integration, 47.99, 60.00

Vector-valued Processes

Henry Helson , David Lowdenslager

Berkeley Symposium on Mathematical Statistics and Probability Vol. 4.2, 203-212 (1961). Open Access

KEYWORDS: Multivariate prediction problem, Moving average, Szegö theorem, 60.50

On Sequences of Sums of Independent Random Vectors

Wassily Hoeffding

Berkeley Symposium on Mathematical Statistics and Probability Vol. 4.2, 213-226 (1961). Open Access

KEYWORDS: Absorption, Convergence, Multidimensional distribution, 60.40, 60.30

Wiener Integral and Feynman Integral

Kiyosi Itô

Berkeley Symposium on Mathematical Statistics and Probability Vol. 4.2, 227-238 (1961). Open Access

KEYWORDS: Physics, Quantum mechanics, 60.75

Spectral Analysis of Stationary Gaussian Processes

Shizuo Kakutani

Berkeley Symposium on Mathematical Statistics and Probability Vol. 4.2, 239-247 (1961). Open Access

KEYWORDS: Multiplicative unitary transformation, Homogeneous chaos, Symmetric tensor product, 60.50

Occupation Time Laws for Birth and Death Processes

Samuel Karlin , James McGregor

Berkeley Symposium on Mathematical Statistics and Probability Vol. 4.2, 249-272 (1961). Open Access

KEYWORDS: Stationary Markov process, Spectral measure, Convergence, Sojourn time, 60.67

An Extension of the Lebesgue Measure of Linear Sets

Paul Lévy

Berkeley Symposium on Mathematical Statistics and Probability Vol. 4.2, 273-287 (1961). Open Access

KEYWORDS: Vitali nonmeasurable sets, Hamel function, Independence paradox, 28.13

On the Probability of Large Deviations for the Sums of Independent Variables

Yu. V. Linnik

Berkeley Symposium on Mathematical Statistics and Probability Vol. 4.2, 289-306 (1961). Open Access

KEYWORDS: Local limit theorem, Integral limit theorem, Zone or normal convergence, 60.30

Recent Developments in the Theory of Characteristic Functions

Eugene Lukacs

Berkeley Symposium on Mathematical Statistics and Probability Vol. 4.2, 307-335 (1961). Open Access

KEYWORDS: Frequency function of stable distribution, Unimodality, Polynomial regression, Characterization problem, Infinite divisibility, 60.20

Asymmetric Orientated Percolation on a Plane

J. G. Mauldon

Berkeley Symposium on Mathematical Statistics and Probability Vol. 4.2, 337-345 (1961). Open Access

KEYWORDS: Crystal, Fluid flow, Markov chain, Convergence, 60.90

Lattice Methods and Submarkovian Processes

Jacques Neveu

Berkeley Symposium on Mathematical Statistics and Probability Vol. 4.2, 347-391 (1961). Open Access

KEYWORDS: Perturbation form, 60.60, 60.69

Some Theorems on Characteristic Functions of Probability Distributions

E. J. G. Pitman

Berkeley Symposium on Mathematical Statistics and Probability Vol. 4.2, 393-402 (1961). Open Access

KEYWORDS: Standard deviation, Derivatives, 60.20

The Method of Characteristic Functionals

Yu. V. Prohorov

Berkeley Symposium on Mathematical Statistics and Probability Vol. 4.2, 403-419 (1961). Open Access

KEYWORDS: Topological space, 60.08

Competition Processes

G. E. H. Reuter

Berkeley Symposium on Mathematical Statistics and Probability Vol. 4.2, 421-430 (1961). Open Access

KEYWORDS: Epidemiology, Recurrence, Absorption, 60.60

Independence and Dependence

M. Rosenblatt

Berkeley Symposium on Mathematical Statistics and Probability Vol. 4.2, 431-443 (1961). Open Access

KEYWORDS: Mixing, Ergodicity, Stationarity generated by independence, 60.50

An Application of the Central Limit Theorem

Yu. A. Rozanov

Berkeley Symposium on Mathematical Statistics and Probability Vol. 4.2, 445-454 (1961). Open Access

KEYWORDS: Weak dependence, Strong mixing condition, Spectral measure, stationary process, Log likelihood, Large deviations, Asymptotics, 60.30, 60.40

Remarks on Processes of Calls

Czesaw Ryll-Nardzewski

Berkeley Symposium on Mathematical Statistics and Probability Vol. 4.2, 455-465 (1961). Open Access

KEYWORDS: Ergodic theory, stationary process, Measure preserving recurrence transformation, Queue, Telephony, 60.80

On Some General Renewal Theorems for Nonidentically Distributed Variables

Walter L. Smith

Berkeley Symposium on Mathematical Statistics and Probability Vol. 4.2, 467-514 (1961). Open Access

KEYWORDS: Insistent subsequence of random variables, Lattice sequence, Series of characteristic function, 60.70

Recurrent Random Walk and Logarithmic Potential

Frank Spitzer

Berkeley Symposium on Mathematical Statistics and Probability Vol. 4.2, 515-534 (1961). Open Access

KEYWORDS: Imbeded Markov chain, Fourier analysis, Potential kernel, Harmonic measure, Capacity, Logarithmic potential theory, 60.66

The Transient Behavior of a Single Server Queuing Process with a Poisson Input

Lajos Takács

Berkeley Symposium on Mathematical Statistics and Probability Vol. 4.2, 535-567 (1961). Open Access

KEYWORDS: Virtual waiting time, Busy period, Limiting distribution, 60.80

Generalized Stochastic Processes with Independent Values

K. Urbanik

Berkeley Symposium on Mathematical Statistics and Probability Vol. 4.2, 569-580 (1961). Open Access

KEYWORDS: Schwartz distribution, Pseudonorm, 60.40

An Application of Ergodic Theorems in the Theory of Queues

David M. G. Wishart

Berkeley Symposium on Mathematical Statistics and Probability Vol. 4.2, 581-592 (1961). Open Access

KEYWORDS: Transition operator, 60.80

Second-order Homogeneous Random Fields

A. M. Yaglom

Berkeley Symposium on Mathematical Statistics and Probability Vol. 4.2, 593-622 (1961). Open Access

KEYWORDS: Spectral representation, Random fields or groups, 60.50

On a Class of Infinitesimal Generators and the Integration Problem of Evolution Equations

Kôsaku Yosida

Berkeley Symposium on Mathematical Statistics and Probability Vol. 4.2, 623-633 (1961). Open Access

KEYWORDS: Semigroup of bounded linear operator, Operator theory, Diffusion equation, Temporal inhomogeneity, Fractional power operator, 47.50, 34.95

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