# First passage under stochastic resetting in an interval

## TL;DR

This paper analyzes how stochastic resetting affects the first passage times of a Brownian particle in an interval, revealing conditions where restart expedites trapping and providing detailed probabilistic insights.

## Contribution

It offers a comprehensive analytical framework for understanding first passage under stochastic resetting in an interval, including success-failure dynamics and criteria for efficiency.

## Key findings

- Resetting can reduce mean first passage time under certain conditions.
- Success and failure rates are quantitatively related to splitting probabilities.
- Numerical results support the analytical predictions.

## Abstract

We consider a Brownian particle diffusing in a one dimensional interval with absorbing end points. We study the ramifications when such motion is interrupted and restarted from the same initial configuration. We provide a comprehensive study of the first passage properties of this trapping phenomena. We compute the mean first passage time and derive the criterion upon which restart always expedites the underlying completion. We show how this set-up is a manifestation of a success-failure problem. We obtain the success and failure rates and relate them with the splitting probabilities, namely, the probability that the particle will eventually be trapped on either of the boundaries without hitting the other one. Numerical studies are presented to support our analytic results.