 Strict Kantorovich contractions for Markov chains and Euler schemes with general noiseLu-Jing Huang, Mateusz B. Majka and Jian Wang Stochastic Processes and their Applications, 2022, vol. 151, issue C, 307-341 Abstract: We study contractions of Markov chains on general metric spaces with respect to some carefully designed distance-like functions, which are comparable to the total variation and the standard Lp-Wasserstein distances for p≥1. We present explicit lower bounds of the corresponding contraction rates. By employing the refined basic coupling and the coupling by reflection, the results are applied to Markov chains whose transitions include additive stochastic noises that are not necessarily isotropic. This can be useful in the study of Euler schemes for SDEs driven by Lévy noises. In particular, motivated by recent works on the use of heavy tailed processes in Markov Chain Monte Carlo, we show that chains driven by the α-stable noise can have better contraction rates than corresponding chains driven by the Gaussian noise, due to the heavy tails of the α-stable distribution. Keywords: Markov chain; Strict Kantorovich contractivity; Total variation; Wasserstein distance; Refined basic coupling; Coupling by reflection (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:151:y:2022:i:c:p:307-341 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2022.06.011 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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