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