Mokaedi Lekgari, A Note on Subgeometric Rate Convergence for Ergodic Markov Chains in the Wasserstein Metric, BMSA Volume 17, Bulletin of Mathematical Sciences and Applications (Volume 17) https://www.scipress.com/BMSA.17.40 Abstract: We investigate subgeometric rate ergodicity for Markov chains in the Wasserstein metricand show that the finiteness of the expectation E(i,j)[Σ<sup>τ<sub>△</sub>-1</sup><sub>k=0</sub> <i>r</i>(<i>k</i>)], where τ△ is the hitting time on thecoupling set △ and<i> r</i> 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’. Keywords: Ergodicity, Markov Chains, Wasserstein Metric