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Nonlinearly perturbed stochastic processes
Mälardalen University, School of Education, Culture and Communication. (Mathematics/Applied Mathematics)ORCID iD: 0000-0002-2626-5598
2008 (English)In: Theory of Stochastic Processes, ISSN 0321-3900, Vol. 14, no 3-4, p. 129-164Article in journal (Refereed) Published
Abstract [en]

This paper is a survey of results presented in the recent book [25]1) .This book is devoted to studies of quasi-stationary phenomena innonlinearly perturbed stochastic systems. New methods of asymptoticanalysis for nonlinearly perturbed stochastic processes basedon new types of asymptotic expansions for perturbed renewal equationand recurrence algorithms for construction of asymptotic expansionsfor Markov type processes with absorption are presented.Asymptotic expansions are given in mixed ergodic (for processes) andlarge deviation theorems (for absorption times) for nonlinearly perturbedregenerative processes, semi-Markov processes, and Markovchains. Applications to analysis of quasi-stationary phenomena innonlinearly perturbed queueing systems, population dynamics andepidemic models, and risk processes are presented. The book alsocontains an extended bibliography of works in the area.

Place, publisher, year, edition, pages
2008. Vol. 14, no 3-4, p. 129-164
National Category
Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-23088OAI: oai:DiVA.org:mdh-23088DiVA, id: diva2:669022
Available from: 2013-12-02 Created: 2013-12-02 Last updated: 2017-02-15Bibliographically approved

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Silvestrov, Dmitrii

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