Subdiffusive continuous time random walks with power-law resetting

Abstract

In the present work we revisit the problem of the behavior of a subdiffusive continuous time random walk (CTRW) under resetting. The resetting process is considered as a renewal process with power-law distribution of waiting times between the resetting events. We consider both the case of complete resetting, when an ordinary CTRW starts anew after the resetting event, and the case of incomplete resetting, when the internal memory of CTRW is nor erased by the resetting event, and the CTRW restarts as an aged one. Using a special representation for the waiting time distribution in resetting, we obtained closed-form expressions for the probability density of displacements and for the mean first passage time to a given point under complete resetting, and asymptotic forms for the probability density of displacements (including prefactors) in the case of incomplete resetting.