Differential equation approximations for Markov chains

R. W. R. Darling; J. R. Norris

doi:10.1214/07-ps121

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arXiv · 0710.3269

Differential equation approximations for Markov chains

R. W. R. Darling·J. R. Norris

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Abstract

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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BibTeX RIS

R. W. R. Darling, J. R. Norris. 2008-04-23. Differential equation approximations for Markov chains. https://doi.org/10.1214/07-ps121

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