In the last years, several 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 a discrete-time counterpart of such a theory and to show relationships and dierences with respect to the continuous time case. We present a class of discrete-time semi-Markov chains which can be constructed as time-changed Markov chains and we obtain the related governing convolution type equations. Such processes converge weakly to those in continuous time under suitable scaling limits.

On discrete-time semi-Markov processes / Pachon, Angelica; Polito, Federico; Ricciuti, Costantino. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES B. - ISSN 1553-524X. - (2021), pp. 1-25. [10.3934/dcdsb.2020170]

On discrete-time semi-Markov processes

Polito, Federico
Membro del Collaboration Group
;
Ricciuti, Costantino
Membro del Collaboration Group
2021

Abstract

In the last years, several 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 a discrete-time counterpart of such a theory and to show relationships and dierences with respect to the continuous time case. We present a class of discrete-time semi-Markov chains which can be constructed as time-changed Markov chains and we obtain the related governing convolution type equations. Such processes converge weakly to those in continuous time under suitable scaling limits.
2021
semi-Markov processes; discrete-time chains; discrete fractional operators; time change; fractional Bernoulli process; sibuya counting process
01 Pubblicazione su rivista::01a Articolo in rivista
On discrete-time semi-Markov processes / Pachon, Angelica; Polito, Federico; Ricciuti, Costantino. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES B. - ISSN 1553-524X. - (2021), pp. 1-25. [10.3934/dcdsb.2020170]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1406512
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