Quasi-Stationary Phenomena in Nonlinearly Perturbed Stochastic Systems

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.

Autorentext

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

Zusammenfassung

"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