LIMIT THEOREMS FOR ASSOCIATED RANDOM FIELDS AND RELATED SYSTEMS (Advanced Stat Sci & Applied Probability) - Hardcover

Bulinski Alexander

Hardcover

ISBN 10: 9812709401 ISBN 13: 9789812709400

Publisher: World Scientific Publishing Company, 2007

Synopsis

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 (e.g. the classical Hoeffding lemma, basic electric current theory etc.).

Edition details

• Publisher: World Scientific Publishing Company
• Publication date: 2007
• Language: English
• ISBN 10: 9812709401
• ISBN 13: 9789812709400
• Binding: Hardcover
• Number of pages: 448