First-passage time for randomly flashing diffusion

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Abstract
The mean-first-passage time (MFPT) of a non-Markovian process that switches randomly between deterministic flow and a Fokker-Planck process (i.e., randomly flashing diffusion) is considered. The problem is formulated in an extended phase space in which the corresponding process is Markovian. It is shown that (boundary and natural) conditions for integration of differential equations determining the MFPT depend strongly on the class of domains from which the process is to escape. Exact solutions are obtained for the MFPT of a linear flow driven by randomly flashing white noise. (c) 1995 The American Physical Society