Mean first-passage time in the presence of colored noise: A random-telegraph-signal approach
- 1 April 1991
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 43 (8) , 4167-4174
- https://doi.org/10.1103/physreva.43.4167
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.Keywords
This publication has 18 references indexed in Scilit:
- Uniform convergence to an effective Fokker-Planck equation for weakly colored noisePhysical Review A, 1986
- First-passage times for non-Markovian processes driven by dichotomic Markov noisePhysical Review A, 1986
- First-passage times for non-Markovian processes: Correlated impacts on bound processesPhysical Review A, 1986
- Mean first-passage time of continuous non-Markovian processes driven by colored noisePhysical Review A, 1986
- First-passage times for non-Markovian processesPhysical Review A, 1986
- Functional-calculus approach to stochastic differential equationsPhysical Review A, 1986
- First-passage time problems for non-Markovian processesPhysical Review A, 1985
- External dichotomous noise: The problem of the mean-first-passage timePhysical Review A, 1985
- Activation rates for nonlinear stochastic flows driven by non-Gaussian noisePhysical Review A, 1984
- Non-Markov processes: The problem of the mean first passage timeZeitschrift für Physik B Condensed Matter, 1981