\(V\)-subgeometric ergodicity for a Hastings-Metropolis algorithm (Q1587711)

The authors are interested in the study of the symmetric random-walk Hastings-Metropolis algorithm in situations where the density is not log-concave in the tails. In Section 2 they introduce some definitions and notations and recall the \(V\)-subgeometric drift criterion of Tuominen and Tweedie, and a practical sufficient condition is stated. Then, in Section 3, it is established that the Metropolis algorithm is \(V\)-ergodic at a subgeometrical rate. Finally, in the Appendix, all the proofs are given.