General approach to stochastic resetting

Abstract

We address the effect of stochastic resetting on diffusion and subdiffusion process. For diffusion we find that MSD relaxes to a constant only when the distribution of reset times possess finite mean and variance. In this case, the leading order contribution to the PDF of a Gaussian propagator under resetting exhibits a cusp independent of the specific details of the reset time distribution. For subdiffusion we derive the PDF in Laplace space for arbitrary resetting protocol. Resetting at constant rate allows evaluation of the PDF in terms of H-function. We analyze the steady state and derive the rate function governing the relaxation behavior. For a subdiffusive process the steady state could exist even if the distribution of reset times possesses only finite mean.

References in corpus (7)

• First Passage Under Restart
• The Prabhakar or three parameter Mittag--Leffler function: theory and application
• Dynamical transition in the temporal relaxation of stochastic processes under resetting
• Exact and explicit probability densities for one-sided Levy stable distributions
• Transport properties of random walks under stochastic non-instantaneous resetting
• On relation between generalized diffusion equations and subordination schemes
• Integral decomposition for the solutions of the generalized Cattaneo equation

Cited by in corpus (5)

• The cost of stochastic resetting
• Random walks with stochastic resetting in complex networks: a discrete time approach
• Capture of a diffusing lamb by a diffusing lion when both return home
• Comparing the roles of time overhead and spatial dimensions on optimal resetting rate vanishing transitions, in Brownian processes with potential bias and stochastic resetting
• Squirrels can remember little: A random walk with jump reversals induced by a discrete-time renewal process