Asymptotic Analysis of Random Walks (Hardcover)

K.A. Borovkov

ISBN 10: 052188117X / ISBN 13: 9780521881173

Published by Cambridge University Press, Cambridge, 2008

About this Item

Hardcover. This book focuses on the asymptotic behavior 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, typical examples being ruin probabilities in risk theory, error probabilities in mathematical statistics, and buffer-overflow probabilities in queueing theory. The classical large deviation theory, developed for distributions decaying exponentially fast (or even faster) at infinity, mostly uses analytical methods. If the fast decay condition fails, which is the case in many important applied problems, then direct probabilistic methods usually prove to be efficient. This monograph presents a unified and systematic exposition of the large deviation theory for heavy-tailed random walks. Most of the results presented in the book are appearing in a monograph for the first time. Many of them were obtained by the authors. 'Heavy-tailed' distributions describe claim sizes in insurance, losses in finance, and more. In many applications, critically important events can be represented as 'large deviations' of random walks - computing probabilities of such events is essential. This monograph presents a unified systematic exposition of the large deviations theory for heavy-tailed random walks. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9780521881173

Bibliographic Details

• Title: Asymptotic Analysis of Random Walks (Hardcover)
• Publisher: Cambridge University Press, Cambridge
• Publication Date: 2008
• Language: English
• ISBN 10: 052188117X
• ISBN 13: 9780521881173
• Binding: Hardcover
• Condition: new

About this title

Synopsis

This book focuses on 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, typical examples being ruin probabilities in risk theory, error probabilities in mathematical statistics, and buffer-overflow probabilities in queueing theory. The classical large deviation theory, developed for distributions decaying exponentially fast (or even faster) at infinity, mostly uses analytical methods. If the fast decay condition fails, which is the case in many important applied problems, then direct probabilistic methods usually prove to be efficient. This monograph presents a unified and systematic exposition of the large deviation theory for heavy-tailed random walks. Most of the results presented in the book are appearing in a monograph for the first time. Many of them were obtained by the authors.

About the Authors

Alexander Borovkov works at the Sobolev Institute of Mathematics in Novosibirsk.

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