Properties of additive functionals of Brownian motion with resetting.
We study the distribution of time-additive functionals of reset Brownian motion, a variation of normal Brownian motion in which the path is interrupted at a given rate according to a Poisson process and placed back to a given reset position. For three examples of functionals (occupation time, area, absolute area), we investigate the effect of the resetting by computing various moments and distributions, using a recent result that links the generating function with resetting to the generating function without reset. We also derive a general variational formula for the large deviation rate function, which we use to analyze two different large deviation regimes appearing in the presence of resetting.
Publisher URL: http://arxiv.org/abs/1801.09909