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Published on: April 19, 2019
One-dimensional telegraphic process with noninstantaneous stochastic resetting
1Dipartimento di Scienza e Alta Tecnologia and Center for Nonlinear and Complex Systems, Università degli studi dell'Insubria, Via Valleggio 11, 22100 Como, Italy and I.N.F.N. Sezione di Milano, Via Celoria 16, 20133 Milano, Italy.
Abstract:
In this paper, we consider the one-dimensional dynamical evolution of a particle traveling at constant speed and performing, at a given rate, random reversals of the velocity direction. The particle is subject to stochastic resetting, meaning that at random times it is forced to return to the starting point. Here we consider a return mechanism governed by a deterministic law of motion, so that the time cost required to return is correlated to the position occupied at the time of the reset. We show that in such conditions the process reaches a stationary state which, for some kinds of deterministic return dynamics, is independent of the return phase. Furthermore, we investigate the first-passage properties of the system and provide explicit formulas for the mean first-hitting time. Our findings are supported by numerical simulations.
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