Stochastically gated local and occupation times of a Brownian particle
File(s)
Published version
Author(s)
Bressloff, Paul C
Type
Journal Article
Abstract
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 is defined as the amount of time spent by the particle in the positive half of the real line, given that it can only cross the origin when a gate placed at the origin is open; in the closed state the particle is reflected. In both scenarios, the gate randomly switches between the open and closed states according to a two-state Markov process. We derive a stochastic, backward Fokker-Planck equation (FPE) for the moment-generating function of the two types of gated Brownian functional, given a particular realization of the stochastic gate, and analyze the resulting stochastic FPE using a moments method recently developed for diffusion processes in randomly switching environments. In particular, we obtain dynamical equations for the moment-generating function, averaged with respect to realizations of the stochastic gate.
Date Issued
2017-01
Date Acceptance
2017-01-01
Citation
Physical Review E, 2017, 95 (1)
ISSN
2470-0045
Publisher
American Physical Society (APS)
Journal / Book Title
Physical Review E
Volume
95
Issue
1
Copyright Statement
©2017 American Physical Society
Identifier
http://dx.doi.org/10.1103/physreve.95.012130
Publication Status
Published
Article Number
012130
Date Publish Online
2017-01-19