The one-dimensional telegraphic process with noninstantaneous stochastic resetting

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.

21 pages, 8 figures

References in corpus (12)

• Statistical Mechanics of Interacting Run-and-Tumble Bacteria
• First Passage Under Restart
• First order transition for the optimal search time of Lévy flights with resetting
• Optimal mean first-passage time for a Brownian searcher subjected to resetting: experimental and theoretical results
• Diffusion with resetting in arbitrary spatial dimension
• Dynamical transition in the temporal relaxation of stochastic processes under resetting
• Monotonous continuous-time random walks with drift and stochastic reset events
• Transport properties of random walks under stochastic non-instantaneous resetting
• Stochastic resetting in underdamped Brownian motion
• Continuous-time random walks with reset events: Historical background and new perspectives
• Non-crossing run-and-tumble particles on a line
• Anomalous diffusion in random-walks with memory-induced relocations