English

Differential equation approximations for Markov chains

Probability 2008-04-23 v2

Abstract

We formulate some simple conditions under which a Markov chain may be approximated by the solution to a differential equation, with quantifiable error probabilities. The role of a choice of coordinate functions for the Markov chain is emphasised. The general theory is illustrated in three examples: the classical stochastic epidemic, a population process model with fast and slow variables, and core-finding algorithms for large random hypergraphs.

Keywords

Cite

@article{arxiv.0710.3269,
  title  = {Differential equation approximations for Markov chains},
  author = {R. W. R. Darling and J. R. Norris},
  journal= {arXiv preprint arXiv:0710.3269},
  year   = {2008}
}

Comments

Published in at http://dx.doi.org/10.1214/07-PS121 the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org)

R2 v1 2026-06-21T09:33:02.165Z