Differential equation approximations for Markov chains

Differential equation approximations for Markov chains

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 variab...

7 Differential Equation Approximations for Markov Chains

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 c...

Approximations of Quasistationary Distributions for Markov Chains

We consider a simple and widely used method for evaluating quasistationary distributions of continuous time Markov chains. The infinite state space is replaced by a large, but finite approximation, which is used to evaluate a candidate distribution. We give some conditions under which the method works, and describe some important pitfalls. μ-subinvariant measures; conditioned processes; limitin...

Blackwell Spaces and -Approximations of Markov Chains

Approximations for the Entropy for Functions of Markov Chains

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