Subgeometric rates of convergence of Markov processes in the Wasserstein metric

By Oleg Butkovsky. 2012

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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.

Subfields: Applied Mathematics, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7dbbacf19c8e6340875f81e56a5ee28522c92f6a

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Citations in the corpus

Quantitative Harris-type theorems for diffusions and McKean–Vlasov processes (2016, background): “It should be mentioned that subgeometric ergodicity of Markov processes has been studied by many others authors in various settings; see [8, 17, 24, 34, 43, 50, 58, 59] and the references therein.”
Generalized couplings and ergodic rates for SPDEs and other Markov models (2018, methodology): “As mentioned above, [23] and subsequent works [6], [12], [25, Chapter 4] provide sufficient conditions for convergence of the law of a Markov process to its invariant measure in Wd for properly chosen d.”
Quantitative contraction rates for Markov chains on general state spaces (2018, background): “in [23, 24, 3, 19] to study properties of Markov chains and diffusion processes.”