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Asymptotic Analysis of Random Walks Heavy-Tailed Distributions

ISBN-10: 052188117X

ISBN-13: 9780521881173

Edition: 2008

Authors: A. A. Borovkov, K. A. Borovkov

List price: $247.00
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Description:

This book is devoted to studying the asymptotic behaviour of the probabilities of large deviations of the trajectories of random walks, with 'heavy-tailed' (in particular, regularly varying, sub- and semiexponential) jump distributions. Large deviation probabilities are of great interest in numerous applied areas, with typical examples being ruin probabilities in risk theory, error probabilities in mathematical statistics, and buffer overflow probabilities in queueing theory. The classical large deviations theory, developed for exponentially fast (or even faster) decaying at infinity distributions, mostly uses analytical methods. If the fast decay condition fails, which is the case in many important applied problems, then mostly direct probabilistic methods prove to be more efficient. This monograph presents a unified and systematic exposition of the large deviations theory for heavy-tailed random walks, based on a common approach, with a large number of new results.
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Book details

List price: $247.00
Copyright year: 2008
Publisher: Cambridge University Press
Publication date: 6/12/2008
Binding: Hardcover
Pages: 656
Size: 6.50" wide x 9.50" long x 1.75" tall
Weight: 2.662
Language: English

Konstantin Borovkov is a staff member in the Department of Mathematics and Statistics at the University of Melbourne.

Introduction
Preliminaries
Random walks with jumps having no finite first moment
Random walks with finite mean and infinite variance
Random walks with jumps having finite variance
Random walks with semiexponential jump distributions
Random walks with exponentially decaying distributions
Asymptotic properties of functions of distributions
On the asymptotics of the first hitting times
Large deviation theorems for sums of random vectors
Large deviations in the space of trajectories
Large deviations of sums of random variables of two types
Non-identically distributed jumps with infinite second moments
Non-identically distributed jumps with finite variances
Random walks with dependent jumps
Extension to processes with independent increments
Extensions to generalised renewal processes
Bibliographic notes
Index of notations
Bibliography