Resetting evanescent one-dimensional random walk and diffusion

Abstract

Resetting has emerged as a cross-cutting theme in stochastic processes in physics, biology, chemistry, engineering, economics, and other areas. Previous works on stochastic resetting have been done in contexts such as first-passage and search theory, stochastic thermodynamics, optimization theory, animal foraging, protein-DNA interactions, chemical reaction processes, stock-market crashes, and population dynamics. The talk will first discuss generic effects of the introduction of stochastic resetting such as the existence of non-equilibrium steady states, and the non-monotonic dependence of mean first passage times on the resetting rate. New results on the interplay of evanescence or mortality and resetting will be presented. In particular, we will discuss how the introduction of resetting modifies characteristics of evanescent one-dimensional random walks and diffusion processes such as occupation probabilities, eventual exit probabilities, eventual return probabilities, conditional first passage times, and the mean number of visited sites.