Sample paths of white noise in spaces with dominating mixed smoothness

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