## Abstract

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.

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.

Original language | English |
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Article number | 225001 |

Number of pages | 19 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 49 |

DOIs | |

Publication status | Published - 27 Apr 2016 |