Path integral formulation for stochastic resetting in an infinite potential barrier

Abstract

We utilize the path integral formalism in finding an analytic expression for the stationary distribution for the position of a Brownian particle diffusing in an infinite barrier potential landscape while under the influence of a space-independent resetting rate r. In the process, we also find an expression for the propagator prior to the first reset, along with the probability distribution of the first reset time of the particle. We verify the obtained expression for the stationary distribution by comparing with the stationary distribution of a free particle subject to resetting as available in literature. Finally, we also examine the effect of varying the resetting rate r and the diffusion coefficient D to the stationary distribution function.