Reflection couplings and contraction rates for diffusions

2013/05/31 by Andreas Eberle · 2 citations
Mathematics · #math.PR #msc:60H10 #msc:60J60

paper · pdf · doi:10.1007/s00440-015-0673-1

To be published in PTRF. The final publication is available at Springer via http://dx.doi.org/10.1007/s00440-015-0673-1

arxiv created 2015/10/19 · arxiv updated 2015/10/20 · crossref issued 2015/10/26 · crossref published 2015/10/26 · crossref published-online 2015/10/26 · crossref created 2015/10/26 · crossref published-print 2016/12/01 · crossref deposited 2022/05/09 · crossref indexed 2026/08/04

Abstract

We consider contractivity for diffusion semigroups w.r.t. Kantorovich (L¹ Wasserstein) distances based on appropriately chosen concave functions. These distances are inbetween total variation and usual Wasserstein distances. It is shown that by appropriate explicit choices of the underlying distance, contractivity with rates of close to optimal order can be obtained in several fundamental classes of examples where contractivity w.r.t. standard Wasserstein distances fails. Applications include overdamped Langevin diffusions with locally non-convex potentials, products of these processes, and systems of weakly interacting diffusions, both of mean-field and nearest neighbour type.

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