Algorithms of Phase Space Reduction and Asymptotics of Hitting Times for Perturbed Semi-Markov Processes

TL;DR

This paper introduces new asymptotic algorithms for phase space reduction in perturbed semi-Markov processes, providing effective conditions for convergence and formulas for limiting distributions and expectations.

Contribution

It develops novel asymptotic algorithms and recurrent formulas for analyzing perturbed semi-Markov processes, enhancing understanding of their limiting behavior.

Findings

Effective conditions for weak convergence of distributions

Recurrent formulas for normalisation functions and Laplace transforms

Limits for expectations of hitting times

Abstract

The paper presents new asymptotic recurrent algorithms of phase space reduction for regularly and singularly perturbed semi-Markov processes. These algorithms give effective conditions of weak convergence for distributions and convergence of expectations for hitting times as well as recurrent formulas for computing the corresponding normalisation functions, Laplace transforms for limiting distributions and limits for expectations.