Quasi-Stationary Phenomena in Nonlinearly Perturbed Stochastic Systems

✍ Scribed by Mats Gyllenberg; Dmitrii S. Silvestrov

• Publisher: De Gruyter
• Year: 2008
• Tongue: English
• Leaves: 592
• Series: De Gruyter Expositions in Mathematics; 44
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Frontmatter
Contents
Introduction
Chapter 1. Perturbed renewal equation
Chapter 2. Nonlinearly perturbed renewal equation
Chapter 3. Nonlinearly perturbed regenerative processes
Chapter 4. Perturbed semi-Markov processes
Chapter 5. Nonlinearly perturbed semi-Markov processes
Chapter 6. Quasi-stationary phenomena in stochastic systems
Chapter 7. Nonlinearly perturbed risk processes
Chapter 8. Supplements
Backmatter