A Note on Transportation Cost Inequalities for Diffusions with Reflections
Probability
2019-02-12 v2
Abstract
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 diffusions with suitable drifts and diffusions. 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.
Cite
@article{arxiv.1808.02164,
title = {A Note on Transportation Cost Inequalities for Diffusions with Reflections},
author = {Soumik Pal and Andrey Sarantsev},
journal= {arXiv preprint arXiv:1808.02164},
year = {2019}
}
Comments
10 pages. Keywords: Reflected Brownian motion, Wasserstein distance, relative entropy, transportation cost-information inequality, concentration of measure, competing Brownian particles