Central limit theorem and almost sure results for bivariate empirical W 1 distances
Résumé
In this paper we study the behavior of the Wasserstein distance of order 1 (also called Kantorovich distance) between the two marginal empirical measures of a stationary sequence of bi-variate random variables. We give sufficient conditions for the central limit theorem, the compact law of the iterated logarithm and the Maricinkiewicz-Zygmund strong law.
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