期刊
PROBABILITY THEORY AND RELATED FIELDS
卷 166, 期 3-4, 页码 851-886出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s00440-015-0673-1
关键词
Couplings of diffusion processes; Wasserstein distances; Absence of convexity; Concave distance functions; Quantitative bounds for convergence to stationarity
资金
- German Science Foundation through the Hausdorff Center for Mathematics
We consider contractivity for diffusion semigroups w.r.t. Kantorovich ( 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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