Poissonian resetting of subdiffusion in a linear potential

Abstract

Resetting a stochastic process is an important problem describing the evolution of physical, biological and other systems which are continually returned to their certain fixed point. We consider the motion of a subdiffusive particle with a constant drift under Poissonian resetting. In this model the stochastic process is Brownian motion subordinated by an inverse infinitely divisible process (subordinator). Although this approach includes a wide class of subdiffusive system with Poissonian resetting by using different subordinators, each of such systems has a stationary state with the asymmetric Laplace distribution in which the scale and asymmetric parameters depend on the Laplace exponent of the subordinators used. Moreover, the mean time for the particle to reach a target is finite and has a minimum, optimal with respect to the resetting rate. Features of Lévy motion under this resetting and the effect of a linear potential are discussed.

arXiv comment12 pages, 5 figures

References in corpus (12)

• Diffusion with Stochastic Resetting
• Intermittent search strategies
• Levy Flights in External Force Fields: Langevin and Fractional Fokker-Planck Equations, and their Solutions
• Experimental realization of diffusion with stochastic resetting
• Diffusion in a potential landscape with stochastic resetting
• Optimal mean first-passage time for a Brownian searcher subjected to resetting: experimental and theoretical results
• Work fluctuations and Jarzynski equality in stochastic resetting
• Péclet number governs transition to acceleratory restart in drift-diffusion
• Searching fast for a target on a DNA without falling to traps
• On subdiffusive continuous time random walks with stochastic resetting
• Fractional dynamics from the ordinary Langevin equation
• Asymmetric Stochastic Resetting: Modeling Catastrophic Events