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Nonlinearly Perturbed Stochastic Processes and Systems

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Mathematical and Statistical Models and Methods in Reliability

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Abstract

This paper is a survey of results presented in the recent book Gyllenberg and Silvestrov [GS08].1 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.

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Author information

Authors and Affiliations

  1. Stockholm University, Stockholm, Sweden

    Dmitrii S. Silvestrov

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  1. Dmitrii S. Silvestrov
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Correspondence to Dmitrii S. Silvestrov .

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Editors and Affiliations

  1. Department of Applied Mathematics, Gubkin Russian State University of Oil a, Leninskii Prospekt 65, Moskva, 117917, Russian Federation

    V.V. Rykov

  2. McMaster University, Department of Mathematics and Statistics, 1280 Main Street West, Hamilton, L8S 4K1, Ontario, Canada

    N. Balakrishnan

  3. Université Victor Segalen Bordeaux 2, I’lnstitut de Mathématiques de Bordeaux, Bordeaux Cedex, 33076, France

    M.S. Nikulin

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Silvestrov, D.S. (2010). Nonlinearly Perturbed Stochastic Processes and Systems. In: Rykov, V., Balakrishnan, N., Nikulin, M. (eds) Mathematical and Statistical Models and Methods in Reliability. Statistics for Industry and Technology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4971-5_2

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