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.
"Differential equation approximations for Markov chains." Probab. Surveys 5 37 - 79, 2008. https://doi.org/10.1214/07-PS121