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    Asymptotic Analysis of Random Walks: Heavy-tailed Distributions (Encyclopedia of Mathematics and Its Applications) (Hardback) By (author) A. A. Borovkov, By (author) K.A. Borovkov

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    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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  • Full bibliographic data for Asymptotic Analysis of Random Walks

    Title
    Asymptotic Analysis of Random Walks
    Subtitle
    Heavy-tailed Distributions
    Authors and contributors
    By (author) A. A. Borovkov, By (author) K.A. Borovkov
    Physical properties
    Format: Hardback
    Number of pages: 656
    Width: 156 mm
    Height: 234 mm
    Thickness: 48 mm
    Weight: 1,220 g
    Language
    English
    ISBN
    ISBN 13: 9780521881173
    ISBN 10: 052188117X
    Classifications

    BIC E4L: MAT
    Nielsen BookScan Product Class 3: S7.8
    B&T Book Type: NF
    B&T Modifier: Region of Publication: 01
    B&T Modifier: Text Format: 42
    B&T Modifier: Academic Level: 01
    BIC subject category V2: PBT
    B&T General Subject: 710
    B&T Modifier: Continuations: 02
    LC classification: QA
    Ingram Subject Code: MA
    Libri: I-MA
    Abridged Dewey: 515
    B&T Approval Code: A51150000
    BISAC V2.8: MAT029000
    LC subject heading:
    B&T Approval Code: A51400000
    Warengruppen-Systematik des deutschen Buchhandels: 16270
    BIC subject category V2: PBK
    B&T Merchandise Category: UP
    BISAC V2.8: MAT034000, MAT003000, MAT007000
    DC22: 519.282
    LC subject heading:
    Thema V1.0: PBT, PBK
    Edition statement
    New.
    Illustrations note
    5 b/w illus.
    Publisher
    CAMBRIDGE UNIVERSITY PRESS
    Imprint name
    CAMBRIDGE UNIVERSITY PRESS
    Publication date
    30 June 2008
    Publication City/Country
    Cambridge
    Author Information
    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.
    Review quote
    'This book is a worthy tribute to the amazing fecundity of the structure of random walks!' Mathematical Reviews '... an up-to-date, unified and systematic exposition of the field. Most of the results presented are appearing in a monograph for the first time and a good proportion of them were obtained by the authors. ... The book presents some beautiful and useful mathematics that may attract a number of probabilists to the large deviations topic in probability.' EMS Newsletter
    Table of contents
    Introduction; 1. Preliminaries; 2. Random walks with jumps having no finite first moment; 3. Random walks with finite mean and infinite variance; 4. Random walks with jumps having finite variance; 5. Random walks with semiexponential jump distributions; 6. Random walks with exponentially decaying distributions; 7. Asymptotic properties of functions of distributions; 8. On the asymptotics of the first hitting times; 9. Large deviation theorems for sums of random vectors; 10. Large deviations in the space of trajectories; 11. Large deviations of sums of random variables of two types; 12. Non-identically distributed jumps with infinite second moments; 13. Non-identically distributed jumps with finite variances; 14. Random walks with dependent jumps; 15. Extension to processes with independent increments; 16. Extensions to generalised renewal processes; Bibliographic notes; Index of notations; Bibliography.