A note on transportation cost inequalities for diffusions with reflections

[摘要] We prove that reflected Brownian motion with normal reflections in a convex domain satisfies a dimension free Talagrand type transportation cost-information inequality. The result is generalized to other reflected diffusion processes with suitable drift and diffusion coefficients. We apply this to get such an inequality for interacting Brownian particles with rank-based drift and diffusion coefficients such as the infinite Atlas model. This is an improvement over earlier dimension-dependent results.

[学科分类] 统计和概率

[关键词] reflected Brownian motion;Wasserstein distance;relative entropy;transportation cost-information inequality;concentration of measure;competing Brownian particles