Differential equation approximations for Markov chains

R. W. R. Darling, J. R. Norris

Published 2007-10-17, updated 2008-04-23Version 2

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.