Quasi-Stationary Phenomena in Nonlinearly Perturbed Stochastic Systems

Mats Gyllenberg; Dmitrii S. Silvestrov

Published by De Gruyter 2008

Quasi-Stationary Phenomena in Nonlinearly Perturbed Stochastic Systems

Mats Gyllenberg and Dmitrii S. Silvestrov

Volume 44 in the series De Gruyter Expositions in Mathematics

https://doi.org/10.1515/9783110208252

Overview
Contents

About this book

The book is devoted to studies of quasi-stationary phenomena in nonlinearly perturbed stochastic systems. New methods of asymptotic analysis for nonlinearly perturbed stochastic processes based on new types of asymptotic expansions for perturbed renewal equation and recurrence algorithms for construction of asymptotic expansions for Markov type processes with absorption are presented. Asymptotic expansions are given in mixed ergodic (for processes) and large deviation theorems (for absorption times) for nonlinearly perturbed regenerative processes, semi-Markov processes, and Markov chains. Applications to analysis of quasi-stationary phenomena in nonlinearly perturbed queueing systems, population dynamics and epidemic models, and for risk processes are presented. The book also contains an extended bibliography of works in the area. It is an essential reference for theoretical and applied researchers in the field of stochastic processes and their applications and may be also useful for doctoral and advanced undergraduate students.

Author / Editor information

Mats Gyllenberg, University of Helsinki, Finland; Dmitrii S. Silvestrov, Mälardalen University, Sweden.

Reviews

"Besides of an original material the book contains a reach reference information on processes what a dealt with, and also a wide bibliography (1094 items) on affected theme."
B. P. Harlamow in: Zentralblatt Math 1/2010

"It is an essential reference for theoretical and applied researchers in the field of stochastic processes and their applications that will contribute to the continuing extensive studies in the area and remain relevant for years to come."
In: Enseignement Mathematique 2/2009

Topics

Frontmatter Requires Authentication Unlicensed Licensed Download PDF	i
Contents Requires Authentication Unlicensed Licensed Download PDF	xi
Introduction Requires Authentication Unlicensed Licensed Download PDF	1
Chapter 1. Perturbed renewal equation Requires Authentication Unlicensed Licensed Download PDF	21
Chapter 2. Nonlinearly perturbed renewal equation Requires Authentication Unlicensed Licensed Download PDF	73
Chapter 3. Nonlinearly perturbed regenerative processes Requires Authentication Unlicensed Licensed Download PDF	103
Chapter 4. Perturbed semi-Markov processes Requires Authentication Unlicensed Licensed Download PDF	165
Chapter 5. Nonlinearly perturbed semi-Markov processes Requires Authentication Unlicensed Licensed Download PDF	257
Chapter 6. Quasi-stationary phenomena in stochastic systems Requires Authentication Unlicensed Licensed Download PDF	359
Chapter 7. Nonlinearly perturbed risk processes Requires Authentication Unlicensed Licensed Download PDF	439
Chapter 8. Supplements Requires Authentication Unlicensed Licensed Download PDF	477
Backmatter Requires Authentication Unlicensed Licensed Download PDF	509

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Researchers, Graduate Students of Mathematics; University Libraries
Pages
- Front matter: 12
- Main content: 579
Keywords: Renewal Equation; Nonlinearly Perturbed Regenerative Processes; Semi-Markov Processes; Markov Chains.

eBook

Published: October 31, 2008
ISBN: 9783110208252

Hardcover

Published: September 16, 2008
ISBN: 9783110204377