Limit Theorems For Associated Random Fields And Related Systems
Title | Limit Theorems For Associated Random Fields And Related Systems PDF eBook |
Author | Alexander Bulinski |
Publisher | World Scientific |
Pages | 447 |
Release | 2007-09-05 |
Genre | Mathematics |
ISBN | 9814474576 |
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.).
Multiple Wiener-Ito Integrals
Title | Multiple Wiener-Ito Integrals PDF eBook |
Author | P. Major |
Publisher | Springer |
Pages | 134 |
Release | 2006-11-14 |
Genre | Mathematics |
ISBN | 3540385576 |
Limit Theorems for Random Fields with Singular Spectrum
Title | Limit Theorems for Random Fields with Singular Spectrum PDF eBook |
Author | Nikolai Leonenko |
Publisher | Springer |
Pages | 406 |
Release | 2011-09-29 |
Genre | Mathematics |
ISBN | 9789401146081 |
Stochastic Geometry, Spatial Statistics and Random Fields
Title | Stochastic Geometry, Spatial Statistics and Random Fields PDF eBook |
Author | Evgeny Spodarev |
Publisher | Springer |
Pages | 470 |
Release | 2013-02-11 |
Genre | Mathematics |
ISBN | 3642333052 |
This volume provides a modern introduction to stochastic geometry, random fields and spatial statistics at a (post)graduate level. It is focused on asymptotic methods in geometric probability including weak and strong limit theorems for random spatial structures (point processes, sets, graphs, fields) with applications to statistics. Written as a contributed volume of lecture notes, it will be useful not only for students but also for lecturers and researchers interested in geometric probability and related subjects.
Central Limit Theorems for Associated Random Fields with Applications
Title | Central Limit Theorems for Associated Random Fields with Applications PDF eBook |
Author | Tae-sung Kim |
Publisher | |
Pages | 148 |
Release | 1985 |
Genre | Central limit theorem |
ISBN |
A functional central limit theorem for a strictly stationary associated random field in the general d-dimension case with an added moment condition is proven. Functional central limit theorems for associated random measures are also proven. More specifically, conditions are given that imply weak convergence in the Skorohod topology of a renormalized random measure to the d-dimensional Wiener process. These results are applied to show new functional central limit theorems for doubly stochastic point random fields and Poisson cluster random measures.
Limit Theorems and Some Applications in Statistical Physics
Title | Limit Theorems and Some Applications in Statistical Physics PDF eBook |
Author | Boris Nahapetian |
Publisher | Springer |
Pages | 260 |
Release | 1991-08 |
Genre | Technology & Engineering |
ISBN |
Limit Theorems for Random Fields with Singular Spectrum
Title | Limit Theorems for Random Fields with Singular Spectrum PDF eBook |
Author | Nicolai Leonenko |
Publisher | Springer Science & Business Media |
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.