Open Access
2008 Differential equation approximations for Markov chains
R.W.R. Darling, J.R. Norris
Probab. Surveys 5: 37-79 (2008). DOI: 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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R.W.R. Darling. J.R. Norris. "Differential equation approximations for Markov chains." Probab. Surveys 5 37 - 79, 2008.


Published: 2008
First available in Project Euclid: 23 April 2008

zbMATH: 1189.60152
MathSciNet: MR2395153
Digital Object Identifier: 10.1214/07-PS121

Primary: 05C65
Secondary: 05C80 , 60J75

Rights: Copyright © 2008 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.5 • 2008
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