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Asymptotic analysis of random walks : = heavy-tailed distributions /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Asymptotic analysis of random walks :/ A.A. Borovkov, K.A. Borovkov ; translated by O.B. Borovkova.
Reminder of title:	heavy-tailed distributions /
Author:	Borovkov, A. A.
other author:	Borovkov, K. A.
Description:	1 online resource (xxix, 625 pages) :digital, PDF file(s). :
Notes:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Subject:	Random walks (Mathematics) -
Online resource:	https://doi.org/10.1017/CBO9780511721397
ISBN:	9780511721397 (ebook)

Asymptotic analysis of random walks : = heavy-tailed distributions /
Borovkov, A. A.1931-

Asymptotic analysis of random walks :heavy-tailed distributions /A.A. Borovkov, K.A. Borovkov ; translated by O.B. Borovkova. - 1 online resource (xxix, 625 pages) :digital, PDF file(s). - Encyclopedia of mathematics and its applications ;volume 118. - Encyclopedia of mathematics and its applications ;v. 82..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Preliminaries -- Random walks with jumps having no finite first moment -- Random walks with jumps having finite mean and infinite variance -- Random walks with jumps having finite variance -- Random walks with semiexponential jump distributions -- Large deviations on the boundary of and outside the Cramer zone for random walks with jump distributions decaying exponentially fast -- Asymptotic properties of functions of regularly varying and semiexponential distributions. Asymptotics of the distributions of stopped sums and their maxima. An alternative approach to studying the asymptotics of P(S[subscript n] [is equal to or greater than] x) -- On the asymptotics of the first hitting times -- Integro-local and integral large deviation theorems for sums of random vectors -- Large deviations in trajectory space -- Large deviations of sums of random variables of two types -- Random walks with non-identically distributed jumps in the triangular array scheme in the case of infinite second moment. Transient phenomena -- Random walks with non-identically distributed jumps in the triangular array scheme in the case of finite variances -- Random walks with dependent jumps -- Extension of the results of Chapters 2-5 to continuous-time random processes with independent increments -- Extension of the results of Chapters 3 and 4 to generalized renewal processes.

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: 9780511721397 (ebook)Subjects--Topical Terms:

783164
Random walks (Mathematics)

LC Class. No.: QA274.73 / .B67 2008

Dewey Class. No.: 519.282

Asymptotic analysis of random walks : = heavy-tailed distributions /
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490 1 $a Encyclopedia of mathematics and its applications ; $v volume 118
500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 $a Preliminaries -- Random walks with jumps having no finite first moment -- Random walks with jumps having finite mean and infinite variance -- Random walks with jumps having finite variance -- Random walks with semiexponential jump distributions -- Large deviations on the boundary of and outside the Cramer zone for random walks with jump distributions decaying exponentially fast -- Asymptotic properties of functions of regularly varying and semiexponential distributions. Asymptotics of the distributions of stopped sums and their maxima. An alternative approach to studying the asymptotics of P(S[subscript n] [is equal to or greater than] x) -- On the asymptotics of the first hitting times -- Integro-local and integral large deviation theorems for sums of random vectors -- Large deviations in trajectory space -- Large deviations of sums of random variables of two types -- Random walks with non-identically distributed jumps in the triangular array scheme in the case of infinite second moment. Transient phenomena -- Random walks with non-identically distributed jumps in the triangular array scheme in the case of finite variances -- Random walks with dependent jumps -- Extension of the results of Chapters 2-5 to continuous-time random processes with independent increments -- Extension of the results of Chapters 3 and 4 to generalized renewal processes.
520 $a 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.
650 0 $a Random walks (Mathematics) $3 783164
650 0 $a Asymptotic expansions. $3 528033
700 1 $a Borovkov, K. A. $3 528035
700 1 $a Borovkova, O. B., $e translator. $3 1445989
776 0 8 $i Print version: $z 9780521881173
830 0 $a Encyclopedia of mathematics and its applications ; $v v. 82. $3 833009
856 4 0 $u https://doi.org/10.1017/CBO9780511721397