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Asymptotic Expansions for Power-Exponential Moments of Hitting Times for Nonlinearly Perturbed Semi-Markov Processes
Stockholm University, Faculty of Science, Department of Mathematics.ORCID iD: 0000-0002-2626-5598
(Mälardalen University, Sweden)ORCID iD: 0000-0003-4554-6528
2017 (English)In: Theory of Probability and Mathematical Statistics, ISSN 0094-9000, Vol. 97, p. 171-187Article in journal (Refereed) Published
Abstract [en]

New algorithms for construction of asymptotic expansions for exponential and power-exponential moments of hitting times for  nonlinearly perturbed  semi-Markov processes are presented. The algorithms are based on special techniques of sequential phase space reduction and the systematical use  of operational calculus for Laurent asymptotic expansions applied to moments of hitting times for perturbed semi-Markov processes. These algorithms have an universal character. They can be applied to nonlinearly perturbed semi-Markov processes with an arbitrary asymptotic communicative structure of a phase space. Asymptotic expansions are given in two forms, without and with explicit bounds for remainders. The algorithms are computationally effective, due to a recurrent character of the corresponding computational procedures.

Place, publisher, year, edition, pages
2017. Vol. 97, p. 171-187
Keywords [en]
Semi-Markov process, Nonlinear perturbation, Hitting time, Power-exponential moment, Laurent asymptotic expansion
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:su:diva-149372ISI: 000424422000014OAI: oai:DiVA.org:su-149372DiVA, id: diva2:1161202
Available from: 2017-11-29 Created: 2017-11-29 Last updated: 2018-03-05Bibliographically approved

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Silvestrov, Dmitrii S.Silvestrov, Sergei D.
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