Asymptotic solution of the Kramers-Moyal equation and first-passage times for Markov jump processes
- 1 June 1984
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 29 (6), 3359-3369
- https://doi.org/10.1103/physreva.29.3359
Abstract
We calculate the activation rates of metastable states of general one-dimensional Markov jump processes by calculating mean first-passage times. We employ methods of singular perturbation theory to derive expressions for these rates, utilizing the full Kramers-Moyal expansions for the forward and backward operators in the master equation. We discuss various boundary conditions for the first-passage-time problem, and present some examples. We also discuss the validity of various diffusion approximations to the master equation, and their limitations.Keywords
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