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28 March 2024
 
  » arxiv » 1211.4273

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Subgeometric rates of convergence of Markov processes in the Wasserstein metric
Oleg Butkovsky ;
Date 19 Nov 2012
AbstractWe 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.
Source arXiv, 1211.4273
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