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On a jump-telegraph process driven by an alternating fractional Poisson process

  • Antonio Di Crescenzo (a1) and Alessandra Meoli (a1)


The basic jump-telegraph process with exponentially distributed interarrival times deserves interest in various applied fields such as financial modelling and queueing theory. Aiming to propose a more general setting, we analyse such a stochastic process when the interarrival times separating consecutive velocity changes (and jumps) have generalized Mittag-Leffler distributions, and constitute the random times of a fractional alternating Poisson process. By means of renewal theory-based issues we obtain the forward and backward transition densities of the motion in series form, and prove their uniform convergence. Specific attention is then given to the case of jumps with constant size, for which we also obtain the mean of the process. Finally, we investigate the first-passage time of the process through a constant positive boundary, providing its formal distribution and suitable lower bounds.


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* Postal address: Dipartimento di Matematica, Università di Salerno, Via Giovanni Paolo II, 132, 84084 Fisciano, SA, Italy.
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On a jump-telegraph process driven by an alternating fractional Poisson process

  • Antonio Di Crescenzo (a1) and Alessandra Meoli (a1)


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