Differential equation approximations for Markov chains

Details Differential equation approximations for Markov chains Differential equation approximations for Markov chains

2007-10-17

arxiv.org/abs/0710.3269v2

Probability Surveys 2008, Vol. 5, 37-79

Mathematics

Probability

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

Scientific paper

10.1214/07-PS121

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.

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