混合光滑空间中白噪声的采样路径
Sample Paths of White Noise in Spaces with Dominating Mixed Smoothness
摘要：
证明了白噪声的样本路径是某些Besov空间的元素，该空间具有控制混合光滑性。与各向同性空间不同，这里的正则性不会随着空间维数的增加而变差。因此，白噪声实际上比各向同性空间中已知的尖锐规律性结果更平滑。我们的技术的应用产生了新的结果的泊松和热方程的解的正则性的半空间与边界噪声。主要的新颖性是灵活处理边界奇异性与切向、法向和时间方向上的光滑性之间的相互作用。
英文摘要：
The sample paths of white noise are proved to be elements of certain Besov spaces with dominating mixed smoothness. Unlike in isotropic spaces, here the regularity does not get worse with increasing space dimension. Consequently, white noise is actually much smoother than the known sharp regularity results in isotropic spaces suggest. An application of our techniques yields new results for the regularity of solutions of Poisson and heat equation on the half space with boundary noise. The main novelty is the flexible treatment of the interplay between the singularity at the boundary and the smoothness in tangential, normal and time direction.
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