Asymptotic Expansions for Stationary Distributions of Nonlinearly Perturbed Semi-Markov Processes. I

TL;DR

This paper introduces new algorithms for deriving asymptotic expansions of stationary distributions in nonlinearly perturbed semi-Markov processes, applicable to complex phase space structures, with and without explicit error bounds.

Contribution

It presents a novel sequential phase space reduction technique for constructing asymptotic expansions in semi-Markov processes with arbitrary structures.

Findings

Algorithms successfully produce asymptotic expansions

Explicit bounds for remainders are provided

Applicable to processes with complex phase space structures

Abstract

New algorithms for construction of asymptotic expansions for stationary distributions of nonlinearly perturbed semi-Markov processes with finite phase spaces are presented. These algorithms are based on a special technique of sequential phase space reduction, which can be applied to processes with an arbitrary asymptotic communicative structure of phase spaces. Asymptotic expansions are given in two forms, without and with explicit bounds for remainders.