Continuous time random walks and Lévy walks with stochastic resetting

Abstract

Intermittent stochastic processes appear in a wide field, such as chemistry, biology, ecology, and computer science. This paper builds up the theory of intermittent continuous time random walk (CTRW) and Lévy walk, in which the particles are stochastically reset to a given position with a resetting rate $r$. The mean squared displacements of the CTRW and Lévy walks with stochastic resetting are calculated, uncovering that the stochastic resetting always makes the CTRW process localized and Lévy walk diffuse slower. The asymptotic behaviors of the probability density function of Lévy walk with stochastic resetting are carefully analyzed under different scales of $x$, and a striking influence of stochastic resetting is observed.

arXiv comment10 pages, 5 figures

References in corpus (13)

• Anomalous transport in the crowded world of biological cells
• Diffusion with Stochastic Resetting
• Lévy walks
• First order transition for the optimal search time of Lévy flights with resetting
• Optimal search strategies for hidden targets
• Non-equilibrium steady states of stochastic processes with intermittent resetting
• Stochastic multiplicative processes with reset events
• Scaled Brownian motion with renewal resetting
• Robustness of optimal intermittent search strategies in dimension 1, 2 and 3
• Random walk with random resetting to the maximum
• Non-renewal resetting of scaled Brownian motion
• On subdiffusive continuous time random walks with stochastic resetting
• Infinite densities for Lévy walks

Cited by in corpus (8)

• Brownian motion under intermittent harmonic potentials
• Continuous time random walks under power-law resetting
• Non-equilibrium thermodynamics of diffusion in fluctuating potentials
• Lévy flights and Lévy walks under stochastic resetting
• Lévy walk dynamics in mixed potentials from the perspective of random walk theory
• Stochastic representation of processes with resetting
• Dynamically emergent correlations in Brownian particles subject to simultaneous non-Poissonian resetting protocols
• Gaussian Process and Levy Walk under Stochastic Non-instantaneous Resetting and Stochastic Rest