Dmitrii Silvestrov: Asymptotic Expansions for Stationary and Quasi-Stationary Distributions of Nonlinearly Perturbed Semi-Markov Processes

Abstract:

New algorithms for computing asymptotic expansions for stationary and quasi-stationary distributions of nonlinearly perturbed semi-Markov processes are presented. The algorithms are based on special techniques of sequential phase space reduction and some kind 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 the 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.