Effects of mortality on stochastic search processes with resetting

Mattia Radice

Published 2022-11-29Version 1

We study the first-passage time to the origin of a mortal Brownian particle, with mortality rate $\mu$, diffusing in one dimension. The particle starts its motion from $x>0$ and it is subject to stochastic resetting with constant rate $r$. We first show that the probability of reaching the target is closely related to the mean first-passage time of the corresponding problem in absence of mortality. We then consider the mean and the variance of the first-passage time conditioned on the event that the particle reaches the target before dying. When the average lifetime $\tau_\mu=1/\mu$ satisfies $\tau_\mu>\alpha\tau_D$, where $\tau_D=x^2/(4D)$ is the diffusive time scale and $\alpha\approx1.575$ is a constant, there is a resetting rate $r_\mu^*$ that maximizes the probability, and there may also be a different rate $r_m$ that minimizes the average time of a successful search; on the other hand, for average lifetimes $\tau_\mu<\beta\tau_D$, with $\beta\approx0.2884$, resetting progressively eliminates slower search processes, resulting in decreasing mean first-passage times but also decreasing the probability of success. Intermediate regimes are also considered.