Nonlinearly perturbed stochastic processes
This paper is a survey of results presented in the recent book [25]). 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 expansio...
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| Дата: | 2008 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2008
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| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/4574 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Nonlinearly perturbed stochastic processes / D. Silvestrov // Theory of Stochastic Processes. — 2008. — Т. 14 (30), № 3-4. — С. 129-164. — Бібліогр.: 77 назв.— англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | This paper is a survey of results presented in the recent book [25]). 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 risk processes are presented. The book also contains an extended bibliography of works in the area. |
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