Central limit theorem for Markov processes with spectral gap in the Wasserstein metric
By Tomasz Komorowski, A. Walczuk. 2011
81 citations recorded by the source corpus.
Suppose that {Xt,t≥0} is a non-stationary Markov process, taking values in a Polish metric space E. We prove the law of large numbers and central limit theorem for an additive functional of the form ∫0Tψ(Xs)ds, provided that the dual transition probability semigroup, defined on measures, is strongly contractive in an appropriate Wasserstein metric. Function ψ is assumed to be Lipschitz on E.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/8d221d782540a198cabe816b6c897114eb7b113d
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In Applied Mathematics
- Andrew M. Stuart
- Mateusz B. Majka
- Sandra Jeanne Vollmer
- Andreas Eberle
- Martin Hairer
- Arnaud Guillin
- Jinghai Shao
- Feng-Yu Wang
In Geometry and Topology
Citations in the corpus
- Spectral gaps for a Metropolis–Hastings algorithm in infinite dimensions (2011, methodology): “Because of Lemma 4.1 and arguments from Lemma 3.2, it is straightforward to verify that our assumptions imply those needed for the Wasserstein CLT in Komorowski and Walczuk (2012).”
- Quantitative contraction rates for Markov chains on general state spaces (2018, background): “By general results, such a bound has many important consequences including quantitative convergence to a unique equilibrium [18], upper bounds on biases and variances as well as concentration inequalities for ergodic averages [29, 38], a central limit theorem for ergodic averages [30], robustness un”