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Simple Bounds for the Convergence of Empirical and Occupation Measures in 1-Wasserstein Distance

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1.	Title	Title of document	Simple Bounds for the Convergence of Empirical and Occupation Measures in 1-Wasserstein Distance
2.	Creator	Author's name, affiliation, country	Emmanuel Boissard; Université de Toulouse; France
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Uniform deviations, Transport inequalities.
3.	Subject	Subject classification	60B10, 39B72
4.	Description	Abstract	We study the problem of non-asymptotic deviations between a reference measure and its empirical version, in the 1-Wasserstein metric, under the standing assumption that the reference measure satisfies a transport-entropy inequality. We extend some results of F. Bolley, A. Guillin and C. Villani with simple proofs. Our methods are based on concentration inequalities and extend to the general setting of measures on a Polish space. Deviation bounds for the occupation measure of a contracting Markov chain in 1-Wasserstein distance are also given. Throughout the text, several examples are worked out, including the cases of Gaussian measures on separable Banach spaces, and laws of diffusion processes.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2011-11-15
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/958
10.	Identifier	Digital Object Identifier	10.1214/EJP.v16-958
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 16
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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