First-passage time statistics: Processes driven by Poisson noise
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.
- Publication:
-
Physical Review A
- Pub Date:
- December 1987
- DOI:
- 10.1103/PhysRevA.36.5774
- Bibcode:
- 1987PhRvA..36.5774H
- Keywords:
-
- 05.40.+j