A note on Variance Bounding for continuous time Markov chains

Fabrizio Leisen (1) , Cecilia Prosdocimi

1 UC3M - Universidad Carlos III de Madrid [Madrid]

In this paper the notion of Variance Bounding introduced by Roberts and Rosenthal (2008) is extended to continuous time Markov Chains. Moreover, it is proven that, as in the discrete time case, the notion of Variance Bounding for reversible Markov Chains is equivalent to the existence of a central limit theorem. A connection with the continuous time Peskun ordering, introduced by Leisen and Mira (2008), concludes the paper.

Mots clés: Variance Bounding; Central limit theorems; Peskun ordering

Domaines: Bio-informatique [q-bio.QM]; Bio-Informatique, Biologie Systémique [q-bio.QM]

Fabrizio Leisen, Cecilia Prosdocimi. A note on Variance Bounding for continuous time Markov chains. Statistics and Probability Letters, 2010, 81 (1), pp.153. ⟨10.1016/j.spl.2010.10.009⟩. ⟨hal-00698846⟩