Electronic Communications in Probability

A note on transportation cost inequalities for diffusions with reflections

Soumik Pal and Andrey Sarantsev

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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
Received: 10 August 2018
Accepted: 7 March 2019
First available in Project Euclid: 5 April 2019

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1554429763

Digital Object Identifier
doi:10.1214/19-ECP223

Mathematical Reviews number (MathSciNet)
MR3940196

Zentralblatt MATH identifier
1416.82031

Subjects
Primary: 82C22: Interacting particle systems [See also 60K35] 60H10: Stochastic ordinary differential equations [See also 34F05] 60J60: Diffusion processes [See also 58J65] 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 91G10: Portfolio theory

Keywords
reflected Brownian motion Wasserstein distance relative entropy transportation cost-information inequality concentration of measure competing Brownian particles

Rights
Creative Commons Attribution 4.0 International License.

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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