Diffusion under time-dependent resetting

By Arnab K. Pal, A. Kundu, M. Evans. 2015

237 citations recorded by the source corpus.

We study a Brownian particle diffusing under a time-modulated stochastic resetting mechanism to a fixed position. The rate of resetting r(t) is a function of the time t since the last reset event. We derive a sufficient condition on r(t) for a steady-state probability distribution of the position of the particle to exist. We derive the form of the steady-state distributions under some particular choices of r(t) and also consider the late time relaxation behavior of the probability distribution. We consider first passage time properties for the Brownian particle to reach the origin and derive a formula for the mean first passage time (MFPT). Finally, we study optimal properties of the MFPT and show that a threshold function is at least locally optimal for the problem of minimizing the MFPT.

Subfields: Molecular Biology, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/062f35b3e0809d1c0dba25a89d68dc92005cc5ae

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Molecular Biology

1. Shamik Gupta
2. A. Jayannavar
3. G. Schehr
4. Satya N. Majumdar
5. M. Evans

Citations in the corpus

• Stochastic Resetting: A (Very) Brief Review (2021, background): “[47] considered a Brownian particle diffusing in presence of time-dependent stochastic resetting, whereby the rate of resetting is a function of the time elapsed since the last reset event, Ref.”
• Stochastic resetting and applications (2019, background): “More generally one can define the resetting process through the waiting time distribution ψ(t) between resetting events [54–56,77], i.”