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Quasi-Stationary Phenomena in Nonlinearly Perturbed Stochastic Systems
School of Education, Culture and Communication, Mälardalen University.
Department of Mathematics, University of Helsinki.
2008 (English)Book (Other academic)
Abstract [en]

This 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.


Place, publisher, year, edition, pages
Berlin: Walter de Gruyter , 2008, 1. , 579 p.
, De Gruyter Expositions in Mathemetics, ISSN 0938-6572 ; 44
Keyword [en]
Nonlinear perturbation, quasi-stationary phenomenon, pseudo-stationary phenomenon, stochastic system, renewal equation, asymptotic expansion, ergodic theorem, limit theorem, large deviation, regenerative process, regenerative stopping time, semi-Markov process, Markov chain, absorption time, queuing system, population dynamics, epidemic model, lifetime, risk process, ruin probability, Cramér-Lundberg approximation, diffusion approximation
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
URN: urn:nbn:se:su:diva-43720ISBN: 978-3-11-020437-7OAI: diva2:359304
Available from: 2010-10-27 Created: 2010-10-27 Last updated: 2010-11-18Bibliographically approved

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Silvestrov, Dmitrii
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ReferencesLink to record
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