First-passage time problems for non-Markovian processes

Subtle difficulties encountered with non-Markovian first-crossing problems are emphasized and illustrated by an exact study of a non-Markovian flow driven by exponentially correlated telegraphic noise. The connection with approximative schemes is made and a general inequality is derived. The relationship with the escape rate at a low noise level is clarified and the Markovian limits to white shot noise and white Gaussian noise are presented.