Asymptotic solution of the Kramers-Moyal equation and first-passage times for Markov jump processes

B. J. Matkowsky*, Z. Schuss, C. Knessl, C. Tier, M. Mangel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

45 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)3359-3369
Number of pages11
JournalPhysical Review A
Volume29
Issue number6
DOIs
StatePublished - 1984

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

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