Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 24 (2019), paper no. 21, 11 pp.
A note on transportation cost inequalities for diffusions with reflections
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.
Electron. Commun. Probab., Volume 24 (2019), paper no. 21, 11 pp.
Received: 10 August 2018
Accepted: 7 March 2019
First available in Project Euclid: 5 April 2019
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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
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