| Asymptotic Analysis of Random Walks: Heavy-Tailed Distributions Contributor(s): Borovkov, A. A. (Author), Borovkov, K. A. (Author) |
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ISBN: 052188117X ISBN-13: 9780521881173 Publisher: Cambridge University Press OUR PRICE: $209.95 Product Type: Hardcover - Other Formats Published: June 2008 Annotation: This book is devoted to studying 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, with typical examples being ruin probabilities in risk theory, error probabilities in mathematical statistics, and buffer overflow probabilities in queueing theory. The classical large deviations theory, developed for exponentially fast (or even faster) decaying at infinity distributions, mostly uses analytical methods. If the fast decay condition fails, which is the case in many important applied problems, then mostly direct probabilistic methods prove to be more efficient. This monograph presents a unified and systematic exposition of the large deviations theory for heavy-tailed random walks, based on a common approach, with a large number of new results. |
| Additional Information |
| BISAC Categories: - Mathematics | Probability & Statistics - General - Mathematics | Differential Equations - General |
| Dewey: 519.282 |
| LCCN: 2008298018 |
| Series: Encyclopedia of Mathematics and Its Applications |
| Physical Information: 2" H x 6.5" W x 9.3" (2.7 lbs) 656 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: This book focuses on the asymptotic behavior 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. |