[PDF] Limit Theorems For The Distributions Of The Maxima Of Partial Sums Of Independent Random Variables eBook

Author : Taĭvo Viktorovich Arak
Publisher : American Mathematical Soc.
Page : 236 pages
File Size : 37,57 MB
Release : 1988
Category : Mathematics
ISBN : 9780821831182

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Among the diverse constructions studied in modern probability theory, the scheme for summation of independent random variables occupies a special place. This book presents a study of distributions of sums of independent random variables with minimal restrictions imposed on their distributions.

Author : Alexander Bulinski
Publisher : World Scientific
Page : 447 pages
File Size : 42,82 MB
Release : 2007-09-05
Category : Mathematics
ISBN : 9814474576

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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 : Mark M. Meerschaert
Publisher : John Wiley & Sons
Page : 515 pages
File Size : 49,40 MB
Release : 2001-07-11
Category : Mathematics
ISBN : 0471356298

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A comprehensive introduction to the central limit theory-from foundations to current research This volume provides an introduction to the central limit theory of random vectors, which lies at the heart of probability and statistics. The authors develop the central limit theory in detail, starting with the basic constructions of modern probability theory, then developing the fundamental tools of infinitely divisible distributions and regular variation. They provide a number of extensions and applications to probability and statistics, and take the reader through the fundamentals to the current level of research. In synthesizing results from nearly 200 research papers and presenting them in a self-contained form, authors Meerschaert and Scheffler have produced an accessible reference that treats the central limit theory honestly and focuses on multivariate models. For researchers, it provides an efficient and logical path through a large collection of results with many possible applications to real-world phenomena. Limit Distributions for Sums of Independent Random Vectors includes a coherent introduction to limit distributions and these other features: * A self-contained introduction to the multivariate problem * Multivariate regular variation for linear operators, real-valued functions, and Borel Measures * Multivariate limit theorems: limit distributions, central limit theorems, and related limit theorems * Real-world applications Limit Distributions for Sums of Independent Random Vectors is a comprehensive reference that provides an up-to-date survey of the state of the art in this important research area.

Author : Yu.V. Prokhorov
Publisher : Springer Science & Business Media
Page : 280 pages
File Size : 46,48 MB
Release : 2013-03-14
Category : Mathematics
ISBN : 3662041723

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A collection of research level surveys on certain topics in probability theory by a well-known group of researchers. The book will be of interest to graduate students and researchers.