Abstract:Let $X$ be the solution of a stochastic differential equation in Euclidean space driven by standard Brownian motion, with measurable drift and Sobolev diffusion coefficient. In our main result we show that when the drift is measurable and the diffusion coefficient belongs to an appropriate Sobolev space, the law of $X$ satisfies Talagrand’s inequality with respect to the uniform distance.

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中文翻译：

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具有可测量漂移的 SDE 的二次运输不等式

摘要：设$X$为标准布朗运动驱动的欧几里得空间随机微分方程的解，具有可测漂移和Sobolev扩散系数。在我们的主要结果中，我们表明，当漂移可测量且扩散系数属于适当的 Sobolev 空间时，$X$ 定律满足关于均匀距离的 Talagrand 不等式。

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