Probability Surveys

Differential equation approximations for Markov chains

R.W.R. Darling and J.R. Norris

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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.

Article information

Probab. Surveys, Volume 5 (2008), 37-79.

First available in Project Euclid: 23 April 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05C65: Hypergraphs
Secondary: 60J75: Jump processes 05C80: Random graphs [See also 60B20]


Darling, R.W.R.; Norris, J.R. Differential equation approximations for Markov chains. Probab. Surveys 5 (2008), 37--79. doi:10.1214/07-PS121.

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