Optimization in First-Passage Resetting

Abstract

We investigate classic diffusion with the added feature that a diffusing particle is reset to its starting point each time the particle reaches a specified threshold. In an infinite domain, this process is non-stationary and its probability distribution exhibits rich features. In a finite domain, we define a non-trivial optimization in which a cost is incurred whenever the particle is reset and a reward is obtained while the particle stays near the reset point. We derive the condition to optimize the net gain in this system, namely, the reward minus the cost.

4 pages, 3 figures, revtex 4-1 format. Version 1 contains changes in response to referee comments. Version 2: A missing factor of 2 in an inline formula has been corrected

References in corpus (4)

• First Passage Under Restart
• Random walks with preferential relocations to places visited in the past and their application to biology
• Stochastic Search with Poisson and Deterministic Resetting
• Interacting Brownian Motion with Resetting

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