On the Telegraph Process driven by Geometric Counting Process with Poissonian Resetting

Verasani Gabriella, Università degli Studi della Basilicata

We investigate the effects of the resetting mechanism to the origin for a random motion on the real line characterized by two alternating velocities v1 and v2. We assume that the sequences of random times concerning the motions along each velocity follow two independent geometric counting processes of intensity λ, and that the resetting times are Poissonian with rate ξ > 0. We obtain the probability laws of the stochastic process using the Markov property of the resetting times and the distribution of the intertimes between consecutive veloc- ity changes. We also study the asymptotic distribution of the particle position when (i) λ tends to infinity, and (ii) the time t goes to infinity. Furthermore, we focus on the determination of the moment-generating function and on the main moments of the process. Finally, we analyse the mean-square distance between the process subject to resets and the same process in absence of resets.

Area: CS32 - Stochastic processes with random resetting (Mario Abundo and Antonella Iuliano)

Keywords: telegraph process, geometric counting process, poisson process, resetting

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