On the mean speed of convergence of empirical and occupation measures in Wasserstein distance
On the mean speed of convergence of empirical and occupation measures in Wasserstein distance
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关于 Wasserstein 距离中经验测度和居住测度的平均收敛速度
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Thibaut Le Gouic
中科院分区：
文献类型：
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作者：
Emmanuel Boissard;Thibaut Le Gouic
在这项工作中，我们提供了非渐近界的平均收敛速度的经验措施，在大数定律，Wasserstein距离。我们还考虑了遍历马尔可夫链的占用测度。其中一个动机是概率测度的近似值由量子化支持的测度（量子化问题）。据发现，在几种情况下，经验或占领措施的速率匹配或接近先前已知的最佳量化率。这在无限维高斯测度的例子中特别突出。
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 finitely 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 infinite-dimensional Gaussian measures.