Asymptotic Expansions for Moment Functionals of Perturbed Discrete Time Semi-Markov Processes

TL;DR

This paper develops asymptotic power series expansions for moment functionals of perturbed semi-Markov processes, providing recursive formulas for coefficients, with applications to quasi-stationary distributions.

Contribution

It introduces explicit recursive formulas for asymptotic expansions of moment functionals in perturbed semi-Markov processes, advancing analytical methods in stochastic process perturbation analysis.

Findings

Asymptotic expansions are valid under specified conditions.

Recursive formulas enable explicit computation of expansion coefficients.

Applications to quasi-stationary distributions demonstrate practical relevance.

Abstract

In this paper, we study mixed power-exponential moment functionals of nonlinearly perturbed semi-Markov processes in discrete time. Conditions under which the moment functionals of interest can be expanded in asymptotic power series with respect to the perturbation parameter are given. We show how the coefficients in these expansions can be computed from explicit recursive formulas. In particular, the results of the present paper have applications for studies of quasi-stationary distributions.