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Physical review. E
We generalize the Feynman-Kac formula to analyze the local and occupation times of a Brownian particle moving in a stochastically-gated one-dimensional domain. (i) The gated local time is defined as the amount of time spent by the particle in the neighborhood of a point in space where there is some target that only receives resources from (or detects) the particle when the gate is open; the target does not interfere with the motion of the Brownian particle. (ii) The gated occupation time isdoi:10.1103/physreve.95.012130 pmid:28208407 fatcat:qfd7dg3znnho3iykhurpmtkiem