A generalized accelerated motion driven by the alternating Poisson process and its effect on lifetimes in random environments

Meoli Alessandra, Università degli Studi di Salerno

Abstract We discuss an extension of the randomly accelerated motion introduced in Meoli [3] and defined as the Riemann-Liouville fractional integral of the telegraph signal. Our main contribution is twofold: indeed, we consider two accelerations $a0$ and $a_1\in\mathbb{R}$, with $a_0\neq a_1$, and two rate of reversals $\lambda_0,\lambda_1>0$. When the order of the fractional integral is 2, $a_0=a_1$ and $\lambda_0=\lambda_1$, our process reduces to one-dimensional uniformly accelerated motion described in Conti and Orsingher [1]. Then, we propose a model for systems whose hazard rate function is a realization of this new stochastic process, along the line traced by Di Crescenzo and Martinucci [2]. References [1] P. L. Conti, E. Orsingher, On the distribution of the position of a randomly accelerated particle, Theory of Probability and Mathematical Statistics, 56(1998), 167-174. [2] A. Di Crescenzo, B. Martinucci, On the effect of random alternating perturbations on hazard rates, Scientiae Mathematicae Japonicae, 64(2006), 381-394. [3] A. Meoli, Some Results on Generalized Accelerated Motions Driven by the Telegraph Process. In: Beghin, L., Mainardi, F., Garrappa, R. (eds) Nonlocal and Fractional Operators. SEMA SIMAI Springer Series, vol 26. Springer, 2021.

Area: CS54 - Random motions and first passage times (Alessandra Meoli and Costantino Ricciuti)

Keywords: Accelerated motions, stochastic hazard rates

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