Continuous time random walks under Markovian resetting

Abstract

We investigate the effects of markovian resseting events on continuous time random walks where the waiting times and the jump lengths are random variables distributed according to power law probability density functions. We prove the existence of a non-equilibrium stationary state and finite mean first arrival time. However, the existence of an optimum reset rate is conditioned to a specific relationship between the exponents of both power law tails. We also investigate the search efficiency by finding the optimal random walk which minimizes the mean first arrival time in terms of the reset rate, the distance of the initial position to the target and the characteristic transport exponents.

Submitted to PRE

References in corpus (4)

• First order transition for the optimal search time of Lévy flights with resetting
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• Lévy flights and Lévy walks under stochastic resetting
• Stochastic resetting prevails over sharp restart for broad target distributions
• Optimization of escape kinetics by reflecting and resetting
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• Exact calculation of the mean first-passage time of continuous-time random walks by nonhomogeneous Wiener-Hopf integral equations
• Stochastic resetting in a nonequilibrium environment
• Resetting induced multimodality
• Generalized diffusion process with nonlocal interactions: Continuous time random walk model and stochastic resetting
• Abrupt transitions in the optimization of diffusion with distributed resetting
• First-passage probabilities and invariant distributions of Kac-Ornstein-Uhlenbeck processes
• Non-standard diffusion under Markovian resetting in bounded domains