Optimization in First-Passage Resetting
Benjamin De Bruyne, Julien Randon‐Furling, S. Redner
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 nonstationary and its probability distribution exhibits rich features. In a finite domain, we define a nontrivial 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.
Topics & Concepts
Reset (finance)Domain (mathematical analysis)Particle (ecology)DiffusionPoint (geometry)Feature (linguistics)Statistical physicsComputer scienceProcess (computing)Stationary distributionProbability distributionControl theory (sociology)Applied mathematicsPhysicsMathematicsMathematical analysisArtificial intelligenceQuantum mechanicsStatisticsGeometryMachine learningFinancial economicsLinguisticsControl (management)Operating systemEconomicsOceanographyGeologyPhilosophyMarkov chainDiffusion and Search DynamicsPlasmonic and Surface Plasmon ResearchRNA and protein synthesis mechanisms