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Subgeometric rates of convergence of Markov processes in the Wasserstein metric

2014; Institute of Mathematical Statistics; Volume: 24; Issue: 2 Linguagem: Inglês

10.1214/13-aap922

2168-8737

Oleg Butkovsky,

Stochastic processes and financial applications

We establish subgeometric bounds on convergence rate of general Markov processes in the Wasserstein metric. In the discrete time setting we prove that the Lyapunov drift condition and the existence of a "good" $d$-small set imply subgeometric convergence to the invariant measure. In the continuous time setting we obtain the same convergence rate provided that there exists a "good" $d$-small set and the Douc-Fort-Guillin supermartingale condition holds. As an application of our results, we prove that the Veretennikov-Khasminskii condition is sufficient for subexponential convergence of strong solutions of stochastic delay differential equations.