Asymptotic Analysis of Random Walks
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Asymptotic Analysis of Random Walks by A. A. Borovkov
Book DescriptionThis 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.
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Book DetailsISBN: 9780521881173
(234mm x 156mm x 40mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 12-Jun-2008
Country of Publication: United Kingdom
Books By Author A. A. Borovkov
Mathematical Statistics, Hardback (January 1999)» View all books by A. A. Borovkov
An overview of modern mathematical statistics, this work is succinct and easy to grasp. The mathematical presentation is coherent and rigorous throughout. It presents classical results and methods that form the basis of modern statistics, and examines the foundations of estimation theory, hypothesis testing theory and statistical game theory.
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Author Biography - A. A. Borovkov
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.
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