On the Mean Speed of Convergence of Empirical and Occupation Measures in Wasserstein Distance
نویسنده
چکیده
In this work, we provide non-asymptotic bounds for the average speed of convergence of the empirical measure in the law of large numbers, in Wasserstein distance. We also consider occupation measures of ergodic Markov chains. One motivation is the approximation of a probability measure by nitely supported measures (the quantization problem). It is found that rates for empirical or occupation measures match or are close to previously known optimal quantization rates in several cases. This is notably highlighted in the example of in nite-dimensional Gaussian measures. MSC-class : 60B10, 65C50, 60J05.
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تاریخ انتشار 2012