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.
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)