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We have derived an exact solution for the first passage time probability of a stationary one-dimensional Markoffian random function from an integral equation. A recursion formula for the moments is given for the case that the conditional probability density describing the random function satisfies a Fokker-Planck equation. Various known solutions for special applications (noise, Brownian motion) are shown to be special cases of our solution. The Wiener-Rice series for the recurrence time probability density is derived from a generalization of Schr\"odinger's integral equation, for the case of a two-dimensional Markoffian random function.
A. J. F. Siegert (Thu,) studied this question.