Mean first passage time for bound non-Markovian stochastic processes with superimposed shot noise

Abstract

In a recent paper, Masoliver and Weiss reported exact analytical expressions for the first passage time (FPT) probability distribution to exit a given interval in the case of a free diffusion process subjected to the effect of superimposed shot noise. In the present note we study by computer simulation the more general case of a bound harmonic system driven by colored Gaussian noise and superimposed shot noise. Approximate expressions are derived for the mean first passage time (MFPT) to reach a given absorbing boundary; these theoretical results are found to be in a good agreement with the results of digital simulation.