Asymptotic Analysis of Random Walks: Heavy-Tailed Distributions

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  • Format: Hardcover
  • Copyright: 2008-06-30
  • Publisher: Cambridge University Press

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Supplemental Materials

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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.

Table of Contents

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
Table of Contents provided by Publisher. All Rights Reserved.

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