First-passage time statistics: Processes driven by Poisson noise

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Abstract
A direct derivation for the first-passage time statistics of processes driven by white Poisson noise is given. This derivation illustrates the difficulty of boundary conditions for a Markovian process driven by a non-Gaussian white noise. In order to gain information on the first-passage time distribution of non-Markovian processes, we carry out numerical simulations for a free process driven by colored Poisson noise with rectangular and exponential pulses. We study the case of stationary and nonstationary noise. Gaussian limits, given by a non-Markovian noise and the Ornstein-Uhlenbeck noise, are also analyzed.