Sample Paths of White Noise in Spaces with Dominating Mixed Smoothness

2020/05/21 by Felix Hummel, Hummel, Felix · 1 citation
Mathematics · #42B35 #60G51 #60H30 #FOS: Mathematics #Primary: 60G17 #Probability (math.PR) #Secondary: 60G15 #math.PR #msc:42B35 #msc:60G15 #msc:60G17 #msc:60G51 #msc:60H30

paper · pdf · doi:10.48550/arxiv.2005.10858

29 pages

arxiv created 2020/05/21 · arxiv updated 2020/05/25

Abstract

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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• R-boundedness of Poisson operators

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