First passage times under frequent stochastic resetting

TL;DR

This paper derives the full distribution and moments of first passage times in stochastic search processes under frequent resetting, applicable to various resetting distributions and validated through examples.

Contribution

It provides a comprehensive analytical framework for first passage times under frequent stochastic resetting, extending to diverse resetting time distributions.

Findings

Errors of the approximations decay exponentially in diffusive search scenarios.

Results are applicable to a broad class of systems with different resetting distributions.

The approach accurately predicts first passage times with minimal error.

Abstract

We determine the full distribution and moments of the first passage time for a wide class of stochastic search processes in the limit of frequent stochastic resetting. Our results apply to any system whose short-time behavior of the search process without resetting can be estimated. In addition to the typical case of exponentially distributed resetting times, we prove our results for a wide array of resetting time distributions. We illustrate our results in several examples and show that the errors of our approximations vanish exponentially fast in typical scenarios of diffusive search.