Asymptotic Expansions for Moment Functionals of Perturbed Discrete Time Semi-Markov Processes
In this paper we study moment functionals of mixed power-exponential type for non-linearly 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.
KeywordsSemi-Markov process Perturbation Asymptotic expansion Renewal equation Solidarity property First hitting time
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