Electronic Communications in Probability

A note on transportation cost inequalities for diffusions with reflections

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 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.

Article information

Source
Electron. Commun. Probab., Volume 24 (2019), paper no. 21, 11 pp.

Dates
Accepted: 7 March 2019
First available in Project Euclid: 5 April 2019

https://projecteuclid.org/euclid.ecp/1554429763

Digital Object Identifier
doi:10.1214/19-ECP223

Mathematical Reviews number (MathSciNet)
MR3940196

Zentralblatt MATH identifier
1416.82031

Citation

Pal, Soumik; Sarantsev, Andrey. A note on transportation cost inequalities for diffusions with reflections. Electron. Commun. Probab. 24 (2019), paper no. 21, 11 pp. doi:10.1214/19-ECP223. https://projecteuclid.org/euclid.ecp/1554429763

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