Differential equation approximations for Markov chains

  title={Differential equation approximations for Markov chains},
  author={R. W. R. Darling},
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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Cores and cycles in random hypergraphs

  • R.W.R. Darling, J. R. Norris
  • In preparation,
  • 2008
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Limit theorems for stochastic processes, volume 288 of Grundlehren der Mathematischen Wissenschaften

  • Jean Jacod, Albert N. Shiryaev
  • 2003

Stochastic approximation and recursive algorithms and applications

  • Harold J. Kushner, G. George Yin
  • 2003

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