Reflection couplings and contraction rates for diffusions

• 成果类型: Article
• 署名作者: Eberle, Andreas
• 署名单位: University of Bonn
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-015-0673-1
• 发表日期: 2016
• 页码: 851-886
• 关键词: brownian motions; MARKOV-PROCESSES; spectral gap; CONVERGENCE; domain; EIGENVALUE; cutoff

摘要

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.