Abstract
We derive an exact theory of the mean first-passage time for an arbitrary one-dimensional dynamical system driven by a multiplicative external noise with finite correlation time (colored noise). Three different cases of colored noise are discussed: the random telegraph signal, the pre-Gaussian noise, and the Ornstein-Uhlenbeck diffusion process. Using random telegraph signals as a tool, we fully solve the difficult problem of non-Markovian boundary conditions associated with such a problem. The analytic solution with these boundary conditions give a complete solution of the escape time in the presence of colored noise.
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