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.
| ISBN: | 9780521881173 |
| Publication date: | 12th June 2008 |
| Author: | A A Borovkov, K A University of Melbourne Borovkov |
| Publisher: | Cambridge University Press |
| Format: | Hardback |
| Pagination: | 656 pages |
| Series: | Encyclopedia of Mathematics and its Applications |
| Genres: |
Probability and statistics Calculus and mathematical analysis |
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.
Asymptotic Analysis of Random Walks features in the following genres: Probability and statistics, Calculus and mathematical analysis
Asymptotic Analysis of Random Walks is available in Hardback
Asymptotic Analysis of Random Walks was written by A A Borovkov, K A University of Melbourne Borovkov and published by Cambridge University Press
Asymptotic Analysis of Random Walks has 656 pages
Yes it is part of Encyclopedia of Mathematics and its Applications series