First passage under stochastic resetting in an interval

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 on 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.