One way to define the concentration of measure phenomenon is via Talagrand inequalities, also called transportation-information inequalities. That is, a comparison of the Wasserstein distance from the given measure to any other absolutely continuous measure with finite relative entropy. Such transportation-information inequalities were recently established for some stochastic differential equations. Here, we develop a similar theory for some stochastic partial differential equations.

中文翻译：

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随机偏微分方程的Talagrand浓度不等式

定义度量现象集中度的一种方法是通过Talagrand不等式，也称为运输信息不等式。也就是说，将Wasserstein距离从给定量度与具有有限相对熵的任何其他绝对连续量度的比较。最近为一些随机微分方程建立了这种运输信息不等式。在这里，我们为一些随机偏微分方程建立了相似的理论。