Monte Carlo simulation of overdamped motion in a double well potential under the influence of coloured noise

We present a Monte Carlo simulation algorithm for evaluating the stationary probability and the mean and the variance of first passage times in any dynamical system under the influence of additive coloured Gaussian and Marcovian noise (Ornstein-Uhlenbeck process). Our algorithm generates the Ornstein-Uhlenbeck process by a superposition of a finite number of random telegraph processes. We obtain our results from a direct evaluation of the trajectories. We apply our method to the overdamped motion of a particle in a double well potential. We compare our simulation results with various analytic approximations for the stationary probability and the mean first passage times.