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Erschienen in:
Reliability of Semi-Markov Systems with Asymptotic Merging Phase Space Kapitel lesen Erstes Kapitel lesen

2010 | OriginalPaper | Buchkapitel

2. Nonlinearly Perturbed Stochastic Processes and Systems

verfasst von : Dmitrii S. Silvestrov

Erschienen in: Mathematical and Statistical Models and Methods in Reliability

Verlag: Birkhäuser Boston

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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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Vorheriges Kapitel Reliability of Semi-Markov Systems with Asymptotic Merging Phase Space
Nächstes Kapitel On a Copula for Failure Times of System Elements
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Metadaten
Titel
Nonlinearly Perturbed Stochastic Processes and Systems
verfasst von
Dmitrii S. Silvestrov
Copyright-Jahr
2010
Verlag
Birkhäuser Boston
Buch
Mathematical and Statistical Models and Methods in Reliability

Print ISBN: 978-0-8176-4970-8

Electronic ISBN: 978-0-8176-4971-5

Copyright-Jahr: 2010

DOI
https://doi.org/10.1007/978-0-8176-4971-5_2

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