Limit Theorems for Motion in Random Fields
Author | : Tomasz Komorowski |
Publisher | : |
Total Pages | : 140 |
Release | : 1994 |
Genre | : |
ISBN | : |
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Author | : Tomasz Komorowski |
Publisher | : |
Total Pages | : 140 |
Release | : 1994 |
Genre | : |
ISBN | : |
Author | : Aleksandr Vadimovich Bulinski? |
Publisher | : World Scientific |
Total Pages | : 447 |
Release | : 2007 |
Genre | : Mathematics |
ISBN | : 9812709401 |
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.).
Author | : Aleksandr Vadimovich Bulinskii |
Publisher | : World Scientific |
Total Pages | : 447 |
Release | : 2007 |
Genre | : Mathematics |
ISBN | : 981270941X |
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.). 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. Readership: Researchers in modern probability and statistics, graduate students and academic staff of the universities.
Author | : Nikolai Leonenko |
Publisher | : Springer |
Total Pages | : 406 |
Release | : 2011-09-29 |
Genre | : Mathematics |
ISBN | : 9789401146081 |
Author | : Nicolai Leonenko |
Publisher | : Springer Science & Business Media |
Total Pages | : 410 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9401146071 |
This book presents limit theorems for nonlinear functionals of random fields with singular spectrum on the basis of various asymptotic expansions. The first chapter treats basic concepts of the spectral theory of random fields, some important examples of random processes and fields with singular spectrum, and Tauberian and Abelian theorems for covariance function of long-memory random fields. Chapter 2 is devoted to limit theorems for spherical averages of nonlinear transformations of Gaussian and chi-square random fields. Chapter 3 summarises some limit theorems for geometric type functionals of random fields. Limit theorems for the solutions of Burgers' equation with random data via parabolic and hyperbolic rescaling are demonstrated in Chapter 4. Lastly, Chapter 5 deals with some problems for statistical analysis of random fields with singular spectrum. Audience: This book will be of interest to mathematicians who use random fields in engineering or other applications.
Author | : Boris Nahapetian |
Publisher | : Springer |
Total Pages | : 260 |
Release | : 1991-08 |
Genre | : Technology & Engineering |
ISBN | : |
Author | : A. N. Borodin |
Publisher | : American Mathematical Soc. |
Total Pages | : 276 |
Release | : 1995 |
Genre | : Mathematics |
ISBN | : 9780821804384 |
This book examines traditional problems in the theory of random walks: limit theorems for additive and multiadditive functionals defined on a random walk. Although the problems are traditional, the methods presented here are new. The book is intended for experts in probability theory and its applications, as well as for undergraduate and graduate students specializing in these areas.
Author | : Nguyen Van Thu |
Publisher | : |
Total Pages | : |
Release | : 1981 |
Genre | : |
ISBN | : |
Author | : |
Publisher | : Springer-Verlag |
Total Pages | : 246 |
Release | : 2013-04-17 |
Genre | : Technology & Engineering |
ISBN | : 3322934322 |
Author | : Aurel Kleinerman |
Publisher | : |
Total Pages | : 208 |
Release | : 1977 |
Genre | : Limit theorems (Probability theory) |
ISBN | : |