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Nonlinearly Perturbed Stochastic Processes and Systems
Stockholm University, Faculty of Science, Department of Mathematics.
2010 (English)In: Mathematical and Statistical Models  and Methods in Reliability :  Applications to Medicine, Finance,  and Quality Control / [ed] V. Rykov, N. Balakrishnan, M. Nikulin, Boston: Birkhäuser , 2010, 19-37 p.Chapter in book (Other academic)
Abstract [en]

This paper is a survey of results presented in the recent book: Gyllenberg, M., Silvestrov, D., Quasi-Stationary Phenomena in Nonlinearly Perturbed Stochastic Systems. De Gruyter Expositions in Mathematics, 44, Walter de Gruyter, Berlin, 2008. This book is devoted to studies of quasi-stationary phenomena for nonlinearly perturbed stochastic processes and systems. New methods of asymptotic analysis for nonlinearly perturbed stochastic processes based on 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
Boston: Birkhäuser , 2010. 19-37 p.
, Statistics for Industry and Technology
Keyword [en]
Nonlinear perturbation, quasi-stationary phenomenon, pseudo-stationary phenomenon, stochastic process, stochastic system, renewal equa- tion, asymptotic expansion, ergodic theorem, limit theorem, large deviation, regen- erative process, regenerative stopping time, semi-Markov process, Markov chain, ab- sorption time, queueing 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-43780ISBN: 0817649700OAI: diva2:359386
Available from: 2010-10-27 Created: 2010-10-27 Last updated: 2010-12-14Bibliographically approved

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Silvestrov, Dmitrii
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