Title: Fluctuations of Timed Averaged Observables of a Particle in a Confining Field
Author: Netanel Barel
We derive a simple formula for fluctuations of time averaged observables for an over-damped Langevin motion in a confining potential field. We show that for ergodic processes these finite measurement time fluctuations are determined by the Boltzmann factor and independent of the initial condition. As a specific example, we examine the residence time statistics in a given domain. We find a general connection between the occupation time probability in some domain and solutions of the corresponding first passage time problem, which allows us to investigate the fluctuation of the residence time in detail.