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A note on transportation cost inequalities for diffusions with reflections. (English) Zbl 1416.82031
Summary: 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.

MSC:
82C22 Interacting particle systems in time-dependent statistical mechanics
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60J60 Diffusion processes
60K35 Interacting random processes; statistical mechanics type models; percolation theory
91G10 Portfolio theory
60J65 Brownian motion
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