An extension of Peskun ordering to continuous time Markov chains

Peskun ordering is a partial ordering defined on the space of transition matrices of discrete time Markov chains. If the Markov chains are reversible with respect to a common stationary distribution "greek Pi", Peskun ordering implies an ordering on the asymptotic variances of the resulting Markov chain Monte Carlo estimators of integrals with respect to "greek Pi". Peskun ordering is also relevant in the framework of time-invariance estimating equations in that it provides a necessary condition for ordering the asymptotic variances of the resulting estimators. In this paper Peskun ordering is extended from discrete time to continuous time Markov chains. Key words and phrases: Peskun ordering, Covariance ordering, Effciency ordering, MCMC, time-invariance estimating equations, asymptotic variance, continuous time Markov chains.