Diffusion under time-dependent resetting

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.

• Publication year

  2015

• Venue

  Journal of Physics A: Mathematical and Theoretical

• Publication date

  2015-12-27

• Fields of study

  Mathematics, Physics

• Identifiers
  DOI 10.1088/1751-8113/49/22/225001arXiv 1512.08211
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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