Mean first-passage time of heterogeneous telegrapher's process under stochastic resetting

¹ Research Center for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts Bul. Krste Misirkov 2, 1000 Skopje, Macedonia
² Institute of Physics, Faculty of Natural Sciences and Mathematics, Ss. Cyril and Methodius University 1000 Skopje, Macedonia
³ Solid State Institute, Technion - Haifa, 32000, Israel
⁴ Max Planck Institute for the Physics of Complex Systems - Nöthnitzer Str. 38, 01187 Dresden, Germany
⁵ Faculty of Computer Science and Engineering, Ss. Cyril and Methodius University - 1000 Skopje, Macedonia
⁶ Department of Physics, Korea University - Seoul 02841, Korea

Received: 27 August 2024
Accepted: 17 January 2025

Abstract

We study the first-passage time of the heterogeneous telegrapher's process, which is a stochastic process with a multiplicative dichotomic noise and a position-dependent velocity. As special cases we recover results for heterogeneous diffusion in the Stratonovich interpretation, as well as the standard telegrapher's process with a constant velocity. In the framework of the renewal equation approach, we study the survival probability and the first-passage time density. An exact result for the mean first-passage time in the presence of Poissonian stochastic resetting of the particle to the initial position is obtained as well. An optimal resetting rate is obtained. In this case, the mean first-passage time becomes minimal for every power-law exponent of the power-law position-dependent velocity. We have also observed that the optimal resetting rate increases when the power-law exponent of the velocity decreases.