A singular perturbation approach to first passage times for Markov jump processes

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

27 Scopus citations

Abstract

We introduce singular perturbation methods for constructing asymptotic approximations to the mean first passage time for Markov jump processes. Our methods are applied directly to the integrai equation for the mean first passage time and do not involve the use of diffusion approximations. An absorbing interval condition is used to properly account for the possible jumps of the process over the boundary which leads to a Wiener-Hopf problem in the neighborhood of the boundary. A model of unimolecular dissociation is considered to illustrate our methods.

Original languageEnglish (US)
Pages (from-to)169-184
Number of pages16
JournalJournal of Statistical Physics
Volume42
Issue number1-2
DOIs
StatePublished - Jan 1 1986

Keywords

  • First passage time
  • Markov jump process
  • asymptotic expansion
  • master equation
  • singular perturbation

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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