We investigate subgeometric rate ergodicity for Markov chains in the Wasserstein metricand show that the finiteness of the expectation E(i,j)[Στ△-1k=0r(k)], where τ△ is the hitting time on thecoupling set △ and r is a subgeometric rate function, is equivalent to a sequence of Foster-Lyapunovdrift conditions which imply subgeometric convergence in the Wassertein distance. We give an examplefor a ’family of nested drift conditions’.
Bulletin of Mathematical Sciences and Applications (Volume 17)
M. Lekgari "A Note on Subgeometric Rate Convergence for Ergodic Markov Chains in the Wasserstein Metric", Bulletin of Mathematical Sciences and Applications, Vol. 17, pp. 40-45, 2016