Correlated continuous-time random walk with stochastic resetting

Abstract

It is known that the introduction of stochastic resetting in an uncorrelated random walk process can lead to the emergence of a stationary state, i.e. the diffusion evolves towards a saturation state, and a steady Laplace distribution is reached. In this paper, we turn to study the anomalous diffusion of the correlated continuous-time random walk considering stochastic resetting. Results reveal that it displays quite different diffusive behaviors from the uncorrelated one. For the weak correlation case, the stochastic resetting mechanism can slow down the diffusion. However, for the strong correlation case, we find that the stochastic resetting cannot compete with the space-time correlation, and the diffusion presents the same behaviors with the one without resetting. Meanwhile, a steady distribution is never reached.