On discrete-time semi-Markov processes

Angelica Pachon, Federico Polito, Costantino Ricciuti

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    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 differences 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.

    Mathematics Subject Classification: 60K15, 60J10, 60G50, 60G51.
    Original languageEnglish
    Pages (from-to)1499-1529
    Number of pages31
    JournalDiscrete and Continuous Dynamical Systems B
    Issue number3
    Publication statusPublished - 1 Aug 2020


    • Semi-Markov processes
    • discrete-time chains
    • discrete fractional operators
    • time change
    • fractional Bernoulli process
    • sibuya counting process


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