Strong Limit Theorems for Quasi-orthogonal Random Fields
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Total Pages | : 24 |
Release | : 1989 |
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Total Pages | : 24 |
Release | : 1989 |
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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.).
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Total Pages | : 25 |
Release | : 2011 |
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Author | : Lin Zhengyan |
Publisher | : Springer Science & Business Media |
Total Pages | : 204 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 9401730970 |
This volume presents an up-to-date review of the most significant developments in strong Approximation and strong convergence in probability theory. The book consists of three chapters. The first deals with Wiener and Gaussian processes. Chapter 2 is devoted to the increments of partial sums of independent random variables. Chapter 3 concentrates on the strong laws of processes generated by infinite-dimensional Ornstein-Uhlenbeck processes. For researchers whose work involves probability theory and statistics.
Author | : R. Jajte |
Publisher | : Springer |
Total Pages | : 159 |
Release | : 2007-01-05 |
Genre | : Mathematics |
ISBN | : 3540391398 |
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Total Pages | : 562 |
Release | : 1990 |
Genre | : Statistics |
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Author | : Ryszard Jajte |
Publisher | : Springer |
Total Pages | : 122 |
Release | : 2006-12-08 |
Genre | : Mathematics |
ISBN | : 3540475125 |
The noncommutative versions of fundamental classical results on the almost sure convergence in L2-spaces are discussed: individual ergodic theorems, strong laws of large numbers, theorems on convergence of orthogonal series, of martingales of powers of contractions etc. The proofs introduce new techniques in von Neumann algebras. The reader is assumed to master the fundamentals of functional analysis and probability. The book is written mainly for mathematicians and physicists familiar with probability theory and interested in applications of operator algebras to quantum statistical mechanics.
Author | : Oleg Klesov |
Publisher | : Springer |
Total Pages | : 495 |
Release | : 2014-10-13 |
Genre | : Mathematics |
ISBN | : 3662443880 |
Presenting the first unified treatment of limit theorems for multiple sums of independent random variables, this volume fills an important gap in the field. Several new results are introduced, even in the classical setting, as well as some new approaches that are simpler than those already established in the literature. In particular, new proofs of the strong law of large numbers and the Hajek-Renyi inequality are detailed. Applications of the described theory include Gibbs fields, spin glasses, polymer models, image analysis and random shapes. Limit theorems form the backbone of probability theory and statistical theory alike. The theory of multiple sums of random variables is a direct generalization of the classical study of limit theorems, whose importance and wide application in science is unquestionable. However, to date, the subject of multiple sums has only been treated in journals. The results described in this book will be of interest to advanced undergraduates, graduate students and researchers who work on limit theorems in probability theory, the statistical analysis of random fields, as well as in the field of random sets or stochastic geometry. The central topic is also important for statistical theory, developing statistical inferences for random fields, and also has applications to the sciences, including physics and chemistry.
Author | : Nikolai Leonenko |
Publisher | : Springer |
Total Pages | : 406 |
Release | : 2011-09-29 |
Genre | : Mathematics |
ISBN | : 9789401146081 |
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Total Pages | : 1448 |
Release | : 2003 |
Genre | : Mathematics |
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