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.

arXiv commentSubmitted to PRE

References in corpus (20)

• Diffusion with Stochastic Resetting
• Diffusion with Optimal Resetting
• First order transition for the optimal search time of Lévy flights with resetting
• Diffusion under time-dependent resetting
• Diffusion in a potential landscape with stochastic resetting
• First passage under stochastic resetting in an interval
• Optimal first arrival times in Lévy flights with resetting
• First passage and arrival time densities for Lévy flights and the failure of the method of images
• Search with home returns provides advantage under high uncertainty
• Monotonous continuous-time random walks with drift and stochastic reset events
• Resetting processes with non-instanteneous return
• Diffusion with stochastic resetting is invariant to return speed
• Transport properties and first arrival statistics of random searches with stochastic reset times
• First Passage Time Distribution for Anomalous Diffusion
• Transport properties of random walks under stochastic non-instantaneous resetting
• Invariants of motion with stochastic resetting and space-time coupled returns
• On subdiffusive continuous time random walks with stochastic resetting
• Stochastic processes subject to a reset-and-residence mechanism: transport properties and first arrival statistics
• Continuous time random walks under power-law resetting
• Brownian motion under non-instantaneous resetting in higher dimensions

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• First passage under restart for discrete space and time: application to one dimensional confined lattice random walks
• Restart expedites quantum walk hitting times
• Fick-Jacobs description and first passage dynamics for diffusion in a channel under stochastic resetting
• Instability in the quantum restart problem
• Encounter-based approach to diffusion with resetting
• Stochastic resetting and first arrival subjected to Gaussian noise and Poisson white noise
• 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
• Random resetting in search problems
• 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