Overview
- Covers fields which are not available in book form and are spread over the literature
- Provides an accessible introduction to a complicated stochastic model
- A readable overview of one of the most complicated topics on applied probability theory
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Series in Operations Research and Financial Engineering (ORFE)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
About this book
In this monograph the authors give a systematic approach to the probabilistic properties of the fixed point equation X=AX+B. A probabilistic study of the stochastic recurrence equation X_t=A_tX_{t-1}+B_t for real- and matrix-valued random variables A_t, where (A_t,B_t) constitute an iid sequence, is provided. The classical theory for these equations, including the existence and uniqueness of a stationary solution, the tail behavior with special emphasis on power law behavior, moments and support, is presented. The authors collect recent asymptotic results on extremes, point processes, partial sums (central limit theory with special emphasis on infinite variance stable limit theory), large deviations, in the univariate and multivariate cases, and they further touch on the related topics of smoothing transforms, regularly varying sequences and random iterative systems.
The text gives an introduction to the Kesten-Goldie theory for stochastic recurrence equations of the type X_t=A_tX_{t-1}+B_t. It provides the classical results of Kesten, Goldie, Guivarc'h, and others, and gives an overview of recent results on the topic. It presents the state-of-the-art results in the field of affine stochastic recurrence equations and shows relations with non-affine recursions and multivariate regular variation.Similar content being viewed by others
Keywords
Table of contents (5 chapters)
Reviews
“It consists of five sections, five appendixes, a list of abbreviations and symbols, 262 references, and an index. It is a well-written and interesting book, and represents a good material for students and researchers.” (Miroslav M. Ristić, zbMATH 1357.60004, 2017)
Authors and Affiliations
Bibliographic Information
Book Title: Stochastic Models with Power-Law Tails
Book Subtitle: The Equation X = AX + B
Authors: Dariusz Buraczewski, Ewa Damek, Thomas Mikosch
Series Title: Springer Series in Operations Research and Financial Engineering
DOI: https://doi.org/10.1007/978-3-319-29679-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Hardcover ISBN: 978-3-319-29678-4Published: 12 July 2016
Softcover ISBN: 978-3-319-80624-2Published: 30 May 2018
eBook ISBN: 978-3-319-29679-1Published: 04 July 2016
Series ISSN: 1431-8598
Series E-ISSN: 2197-1773
Edition Number: 1
Number of Pages: XV, 320
Number of Illustrations: 4 b/w illustrations, 5 illustrations in colour
Topics: Probability Theory and Stochastic Processes, Statistics for Business, Management, Economics, Finance, Insurance, Economic Theory/Quantitative Economics/Mathematical Methods