2015/12/31 by A. Pal, Arnab Pal, Anupam Kundu +2 · 4 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · Physics and Astronomy · #Brownian motion #Diffusion #Diffusion and Search Dynamics #Distribution (mathematics) #Event (particle physics) #First-hitting-time model #Mathematical analysis #Mathematical and Theoretical Epidemiology and Ecology Models #Mathematics #Particle (ecology) #Physics #Position (finance) #Probability distribution #Quantum mechanics #Reset (finance) #Statistical physics #Statistics #Steady state (chemistry) #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.1088/1751-8113/49/22/225001
published as Journal of Physics A: Mathematical and Theoretical, Volume 49, 225001 (2016) · 15 pages, 4 figures
openalex publication_date 2016/04/28 · arxiv created 2016/05/12 · arxiv updated 2016/05/18 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/06
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.