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On random motions with velocities alternating at Erlang-distributed random times

  • Antonio Di Crescenzo (a1)


We analyse a non-Markovian generalization of the telegrapher's random process. It consists of a stochastic process describing a motion on the real line characterized by two alternating velocities with opposite directions, where the random times separating consecutive reversals of direction perform an alternating renewal process. In the case of Erlang-distributed interrenewal times, explicit expressions of the transition densities are obtained in terms of a suitable two-index pseudo-Bessel function. Some results on the distribution of the maximum of the process are also disclosed.


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Postal address: Dipartimento di Matematica, Università degli Studi della Basilicata, Loc. Macchia Romana, I-85100 Potenza, Italy. Email address:


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On random motions with velocities alternating at Erlang-distributed random times

  • Antonio Di Crescenzo (a1)


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