On discrete-time semi-Markov processes

Angelica Pachon; Federico Polito; Costantino Ricciuti

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arXiv · 1807.07932

On discrete-time semi-Markov processes

Angelica Pachon·Federico Polito·Costantino Ricciuti

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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.

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Angelica Pachon, Federico Polito, Costantino Ricciuti. 2018-07-20. On discrete-time semi-Markov processes. https://arxiv.org/abs/1807.07932

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