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First-Passage Resetting and Optimization
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TL;DR: This work investigates classic diffusion with the added feature that a diffusing particle is reset to its starting point each time the particle reaches a specified threshold, and derives the condition to optimize the net gain in this system, namely, the reward minus the cost.
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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.
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Citations
Intermittent resetting potentials
TL;DR: In this article, the authors studied the non-equilibrium steady states and first passage properties of a Brownian particle with position $X$ subject to an external confining potential of the form $V(X)=\mu|X|$, and that is switched on and off stochastically.
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Mean-performance of sharp restart I: statistical roadmap
Iddo Eliazar,Shlomi Reuveni +1 more
TL;DR: This paper presents a comprehensive mean-performance analysis of sharp restart, and establishes universal criteria that determine when sharp restart improves or worsens mean- performance, i.e., decreases or increases mean first-passage/completion times.
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Random acceleration process under stochastic resetting
TL;DR: In this paper, the authors consider the motion of a randomly accelerated particle in one dimension under stochastic resetting mechanism and derive the expressions for the mean first passage time and the survival probability at large $t.
32
Intermittent resetting potentials
TL;DR: In this article, the authors studied the non-equilibrium steady states and first passage properties of a Brownian particle with position $X$ subject to an external confining potential of the form $V(X)=\mu|X|$, and that is switched on and off stochastically.
15
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