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Differential equation approximations for Markov chains. (English) Zbl 1189.60152
Summary: 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.

MSC:
60J75 Jump processes (MSC2010)
05C65 Hypergraphs
05C80 Random graphs (graph-theoretic aspects)
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