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

TL;DR

This paper develops explicit asymptotic expansions with bounds for stationary distributions of nonlinearly perturbed semi-Markov processes, using a sequential phase space reduction technique applicable to complex structures.

Contribution

It introduces a novel algorithm for asymptotic analysis of stationary distributions in semi-Markov processes with arbitrary phase space structures.

Findings

Explicit asymptotic expansions with upper bounds for remainders

A sequential phase space reduction algorithm

Applicable to processes with complex communicative structures

Abstract

Asymptotic expansions with explicit upper bounds for remainders are given for stationary distributions of nonlinearly perturbed semi-Markov processes with finite phase spaces. The corresponding 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.