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Theory of Probability and Mathematical Statistics

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Asymptotic expansions for power-exponential moments of hitting times for nonlinearly perturbed semi-Markov processes


Authors: D. S. Silvestrov and S. D. Silvestrov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 97 (2017).
Journal: Theor. Probability and Math. Statist. 97 (2018), 183-200
MSC (2010): Primary 60J10, 60J27, 60K15; Secondary 65C40
DOI: https://doi.org/10.1090/tpms/1056
Published electronically: February 21, 2019
MathSciNet review: 3746007
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Abstract: 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 a 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.


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Additional Information

D. S. Silvestrov
Affiliation: Department of Mathematics, Stockholm University, SE-106 81 Stockholm, Sweden
Email: silvestrov@math.su.se

S. D. Silvestrov
Affiliation: Division of Applied Mathematics, Mälardalen University, SE-721 23 Västerås, Sweden
Email: sergei.silvestrov@mdh.se

DOI: https://doi.org/10.1090/tpms/1056
Keywords: Semi-Markov process, nonlinear perturbation, hitting time, power-exponential moment, Laurent asymptotic expansion
Received by editor(s): September 5, 2017
Published electronically: February 21, 2019
Article copyright: © Copyright 2019 American Mathematical Society