Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 49, Issue 22, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8113/49/22/225001
Keywords
Markov processes; stochastic resetting; large deviations
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Funding
- EPSRC [EP/J007404/1]
- Weizmann Institute
- EPSRC [EP/J007404/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/J007404/1] Funding Source: researchfish
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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.
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