Regularity of Gaussian white noise on the d-dimensional torus

2010/10/29 by Mark Veraar, Veraar, Mark
Mathematics · #46E35 #60G15 (Primary) #60G17 (Secondary) #60H40 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR) #math.AP #math.FA #math.PR #msc:46E35 #msc:60G15 #msc:60G17 #msc:60H40

paper · pdf · doi:10.48550/arxiv.1010.6219

arxiv created 2010/11/05 · arxiv updated 2010/11/08

Abstract

In this paper we prove that a Gaussian white noise on the d-dimensional torus has paths in the Besov spaces B^-d/2_p,∞(\T^d) with p∈ [1, ∞). This result is shown to be optimal in several ways. We also show that Gaussian white noise on the d-dimensional torus has paths in a the Fourier-Besov space b^-d/p_p,∞(\T^d). This is shown to be optimal as well.

Related

• Sample Paths of White Noise in Spaces with Dominating Mixed Smoothness
• Multidimensional Lévy White Noises in Weighted Besov Spaces
• Nearly optimal bounds on the Fourier sampling numbers of Besov spaces
• On Besov regularity and local time of the stochastic heat equation
• Regularity of Gaussian Processes on Dirichlet spaces