Asymptotics of rare events in birth-death processes bypassing the exact solutions

Charles R. Doering, Khachik V. Sargsyan, Leonard M. Sander, Eric Vanden-Eijnden

Research output: Contribution to journalArticle

Abstract

We investigate the near-continuum asymptotics of mean first passage times in some one-variable birth-death processes. The particular problem we address is how to extract mean first passage times in the near-continuum limit from their defining finite-difference equations alone. For the simple class of processes we consider here, exact closed-form solutions for the mean first passage time between any two states are available and the near-continuum expansion of these formulae defines the correct limiting behaviour and is used to check the results of asymptotic analysis of the difference equations. We find that in some cases the asymptotic approach does not lead unequivocally to the proper result.

Original languageEnglish (US)
Article number065145
JournalJournal of Physics Condensed Matter
Volume19
Issue number6
DOIs
StatePublished - Feb 14 2007

ASJC Scopus subject areas

  • Materials Science(all)
  • Condensed Matter Physics

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