Simple Bounds for the Convergence of Empirical and Occupation Measures in 1-Wasserstein Distance
Simple Bounds for the Convergence of Empirical and Occupation Measures in 1-Wasserstein Distance
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1-Wasserstein 距离中经验测度和职业测度收敛的简单界限
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发表时间：
2011
期刊：
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通讯作者：
Emmanuel Boissard
中科院分区：
文献类型：
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作者：
Emmanuel Boissard
我们研究了1-Wasserstein度量中的参考测度与其经验版本之间的非渐近偏差问题，假设参考测度满足一个输运熵不等式.推广了F. Bolley，A. Guillin和C.维拉尼简单的证明。我们的方法是基于浓度不等式，并扩展到波兰空间上的措施的一般设置。给出了收缩马氏链在1-Wasserstein距离下的占有测度的偏差界。在整个文本中，几个例子，包括高斯措施的情况下，可分的Banach空间，和法律的扩散过程。
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.