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The sample paths of white noise are proved to be elements of certain Besovspaces with dominating mixed smoothness. Unlike in isotropic spaces, here theregularity does not get worse with increasing space dimension. Consequently,white noise is actually much smoother than the known sharp regularity resultsin isotropic spaces suggest. An application of our techniques yields newresults for the regularity of solutions of Poisson and heat equation on thehalf space with boundary noise. The main novelty is the flexible treatment ofthe interplay between the singularity at the boundary and the smoothness intangential, normal and time direction.

Sample Paths of White Noise in Spaces with Dominating Mixed Smoothness