In this paper, we prove transportation inequalities on the space of continuous paths with respect to the uniform metric, for the law of the solution to a stochastic heat equation defined on \([0,T]\times [0,1]^{d}\). This equation is driven by the Gaussian noise, white in time and colored in space. The proof is based on a new moment inequality under the uniform metric for the stochastic convolution with respect to the time-white and space-colored noise, which is of independent interest.

中文翻译：

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时空和彩色噪声驱动的随机热方程在统一度量下的运输不等式

本文针对统一度量证明了连续路径空间上的运输不等式，这是求解\（[[0，T] \ times [0,1] ^ { d} \）。该方程由高斯噪声驱动，时间为白色，空间为彩色。证明是基于关于时间卷积和时空色噪声的随机卷积的统一度量下的新矩不等式，这是独立引起关注的。