Mean first-passage time for systems driven by pre-Gaussian noise: Natural boundary conditions.

Abstract

In order to determine the mean first-passage time for systems driven by a superposition of suitably scaled independent dichotomous Markovian processes (pre-Gaussian noise), the well-known absorbing boundary conditions must be complemented in the generic case by a novel type of natural boundary conditions. We treat explicitly a linear stochastic flow for the superposition of up to five dichotomous processes and compare the analytic results with a digital simulation for these processes and an Ornstein-Uhlenbeck process.