Abstract
AbstractThe 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.
Funder
Studienstiftung des Deutschen Volkes
Horizon 2020
Technische Universität München
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
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