# Asymptotic Analysis of Random Walks: Heavy-Tailed Distributions

*Centre of Excellence for Mathematics and Statistics of Complex Systems Seminar*

*by Kostya Borovkov*

*Institution:*The University of Melbourne

*Date: Fri 13th March 2009*

*Time: 3:15 PM*

*Location: Theatre 1, ICT Bldg (Grd Floor, 111 Barry St, Carlton)*

*Abstract*: This talk will present a new monograph with the same title by A. A. Borovkov and K. A. Borovkov published in 2008 by Cambridge University Press (ISBN-13: 9780521881173, weight: 1.22 kg).

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.

*For More Information:* Kostya Borovkov borovkov@unimelb.edu.au