Open Access
April 2014 Subgeometric rates of convergence of Markov processes in the Wasserstein metric
Oleg Butkovsky
Ann. Appl. Probab. 24(2): 526-552 (April 2014). DOI: 10.1214/13-AAP922


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.


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Oleg Butkovsky. "Subgeometric rates of convergence of Markov processes in the Wasserstein metric." Ann. Appl. Probab. 24 (2) 526 - 552, April 2014.


Published: April 2014
First available in Project Euclid: 10 March 2014

zbMATH: 1304.60076
MathSciNet: MR3178490
Digital Object Identifier: 10.1214/13-AAP922

Primary: 34K50 , 60J05 , 60J25

Keywords: Lyapunov functions , Markov processes , stochastic delay equations , subgeometric convergence , Wasserstein metric

Rights: Copyright © 2014 Institute of Mathematical Statistics

Vol.24 • No. 2 • April 2014
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