Theory of Probability and Mathematical Statistics
(Teoriya Imovirnostei ta Matematychna Statystyka)
Asymptotic Expansions for Power-Exponential Moments of Hitting Times for Nonlinearly Perturbed Semi-Markov Processes
D. S. Silvestrov, S. D.Silvestrov
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 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.
Keywords: Semi-Markov process, Nonlinear perturbation, Hitting time, Power-exponential moment, Laurent asymptotic expansion
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