2007/10/31 by R. W. R. Darling, James R. Norris, J. R. Norris · 1 citation
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics #math.PR #msc:05C65 #msc:05C80 #msc:60J75
paper · pdf · doi:10.1214/07-ps121
published as Probability Surveys 2008, Vol. 5, 37-79 · Published in at http://dx.doi.org/10.1214/07-PS121 the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2008/01/01 · arxiv created 2008/04/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.