Signed Poisson 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...

Translated Poisson approximation for Markov chains

The paper is concerned with approximating the distribution of a sum W of integer valued random variables Yi, 1 ≤ i ≤ n, whose distributions depend on the state of an underlying Markov chain X. The approximation is in terms of a translated Poisson distribution, with mean and variance chosen to be close to those of W , and the error is measured with respect to the total variation norm. Error boun...

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