Regularity of Gaussian white noise on the d-dimensional torus

• Autorzy: Mark C. Veraar
• Języki publikacji: EN

Abstrakty

EN

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 the Fourier-Besov space $b̂^{-d/p}_{p,∞}(𝕋^d)$. This is shown to be optimal as well.

Kategorie tematyczne

• 60H40: White noise theory
• 60G15: Gaussian processes
• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
• 60G17: Sample path properties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2011
• Tom: 95
• Numer: 1
• Strony: 385-398

Daty

wydano

2011

Twórcy

autor

Mark C. Veraar

• Delft Institute of Applied Mathematics, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands

Identyfikatory

DOI

10.4064/bc95-0-24