01-09-2020
The second, entitled "On Discrete time semi Markov processes" accepted for publication in the Journal “Discrete and Continuos Dynamical Systems Series B” . The paper is joint work with Federico Polito and Constantino Ricciuti of the Department of Mathematics at University of Turin, Italy. 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. They show that a class of discrete-time semi-Markov chains can be seen as time-changed Markov chains and they obtain governing convolution type equations. Such processes converge weakly to those in continuous time under suitable scaling limits. http://dx.doi.org/10.3934/dcdsb.2020170
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