Effects of a moving barrier on the first-passage time of a diffusing particle under stochastic resetting

Abstract

We study a first-passage time problem for a one-dimensional diffusion under stochastic resetting through a moving barrier described by a piecewise affine function. It is shown that the mean first-passage time can be minimized with respect to the resetting rate. However, the mean first-passage time exhibits multiple extrema as a function of the resetting rate, depending on the choice of the model parameters. This contrasts with the diffusion with stochastic resetting with static barrier, where only a single minimum exists. We develop a detailed numerical example in the case where the moving barrier is an alternating sequence of a constant function and an affine function with arbitrary slope. It is found that the optimal resetting rate varies discontinuously with the slope.