A note on transportation cost inequalities for diffusions with reflections
Autor: | Andrey Sarantsev, Soumik Pal |
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Rok vydání: | 2019 |
Předmět: |
Statistics and Probability
82C22 60H10 60J60 60K35 91G10 Kullback–Leibler divergence Rank (linear algebra) Type (model theory) transportation cost-information inequality 91G10 01 natural sciences 010104 statistics & probability Mathematics::Probability Dimension (vector space) reflected Brownian motion FOS: Mathematics Wasserstein distance 0101 mathematics Diffusion (business) Brownian motion 60J60 Mathematics Concentration of measure relative entropy Probability (math.PR) 010102 general mathematics Mathematical analysis concentration of measure Reflected Brownian motion 60K35 competing Brownian particles 60H10 82C22 Statistics Probability and Uncertainty Mathematics - Probability |
Zdroj: | Electron. Commun. Probab. |
ISSN: | 1083-589X |
DOI: | 10.1214/19-ecp223 |
Popis: | 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. 10 pages. Keywords: Reflected Brownian motion, Wasserstein distance, relative entropy, transportation cost-information inequality, concentration of measure, competing Brownian particles |
Databáze: | OpenAIRE |
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