On discrete-time semi-Markov processes
Probability
2020-02-24 v2
Abstract
In the last years, many authors studied a class of continuous time semi-Markov processes obtained by time-changing Markov processes by hitting times of independent subordinators. Such processes are governed by integro-differential convolution equations of generalized fractional type. The aim of this paper is to develop the discrete-time version of such a theory. We show that a class of discrete-time semi-Markov chains can be seen as time-changed Markov chains and we obtain governing convolution type equations. Such processes converge weakly to those in continuous time under suitable scaling limits.
Cite
@article{arxiv.1807.07932,
title = {On discrete-time semi-Markov processes},
author = {Angelica Pachon and Federico Polito and Costantino Ricciuti},
journal= {arXiv preprint arXiv:1807.07932},
year = {2020}
}