Limit theorems for associated random fields and related systems / Alexander Bulinski & Alexey Shashkin.

Format:

Book

Author/Creator:

Bulinskiĭ, A. V. (Aleksandr Vadimovich)

Contributor:

Shashkin, A. P. (Alekseĭ Pavlovich)

Louis A. Duhring Fund.

Series:

Advanced series on statistical science & applied probability ; v. 10.

Advanced series on statistical science and applied probability ; v. 10

Language:

English

Subjects (All):

Random fields.

Limit theorems (Probability theory).

Physical Description:

x, 436 pages ; 26 cm.

Place of Publication:

New Jersey : World Scientific, [2007]

Summary:

This volume is devoted to the study of asymptotic properties of wide classes of stochastic systems arising in mathematical statistics, percolation theory, statistical physics and reliability theory Attention is paid not only to positive and negative associations introduced in the pioneering papers by Harris, Lehmann, Esary, Proschan, Walkup, Fortuin, Kasteleyn and Ginibre, but also to new and more general dependence conditions. Naturally, this scope comprises families of independent real valued random variables A Variety of important results and examples of Markov processes, random measures, stable distributions, Ising ferromagnets, interacting particle systems, stochastic differential equations, random graphs and other models are provided. For such random systems, it is worthwhile to establish principal limit theorems of the modern probability theory (central limit theorem for random fields, weak and strong invariance principles, functional law of the iterated logarithm etc) and discuss their applications

There are 434 items in the bibliography

The book is self-contained, provides detailed proofs, for reader's convenience some auxiliary results are included in the Appendix. It is useful for probabilists and statisticians interested in analyzing various stochastic models, for graduate students and academic staff of the universities.

Contents:

Random systems with covariance inequalities

Moment and maximal inequalities

Central limit theorem

Almost sure convergence

Invariance principles

Law of the iterated logarithm

Statistical applications

Integral functionals.

Notes:

Includes bibliographical references (pages 411-430) and indexes.

Local Notes:

Acquired for the Penn Libraries with assistance from the Louis A. Duhring Fund.

ISBN:

9789812709400

9812709401

OCLC:

141187985