Properties of additive functionals of Brownian motion with resetting

Abstract

We study the distribution of additive functionals of reset Brownian motion, a variation of normal Brownian motion in which the path is interrupted at a given rate and placed back to a given reset position. Our goal is two-fold: (1) For general functionals, we derive a large deviation principle in the presence of resetting and identify the large deviation rate function in terms of a variational formula involving large deviation rate functions without resetting. (2) For three examples of functionals (positive occupation time, area and absolute area), we investigate the effect of resetting by computing distributions and moments, using a formula that links the generating function with resetting to the generating function without resetting.

23 pages, 4 figures

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• Exact joint distributions of three global characteristic times for Brownian motion
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• Local large deviation principle for Wiener process with random resetting
• Thermodynamics of quantum-jump trajectories of open quantum systems subject to stochastic resetting
• Short-time large deviations of first-passage functionals for high-order stochastic processes
• Large time probability of failure in diffusive search with resetting in arbitrary dimension--a functional analytic approach