Biased random walks with a truncated stochastic resetting mechanism

Abstract

Inspired by the idea there are no unlimited chances in life, we study a truncated stochastic resetting mechanism that limits the chances of a biased random walker to perform restarts. We study the effects of such mechanism on the first four cumulants of the walker’s occupation probability mass functions. We found that incorporating finite resets to biased random walks temporarily stops the mean and variance from blowing up and introduces temporary spikes to skewness and kurtosis. Our work provides a potential gateway to studying other variants of truncation to resetting and other stochastic switching phenomena.