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Regularity of Gaussian white noise on the $d$-dimensional torus

Volume 95 / 2011

Banach Center Publications 95 (2011), 385-398 MSC: Primary: 60G15; Secondary: 46E35, 60H40, 60G17. DOI: 10.4064/bc95-0-24

Abstract

In this paper we prove that a Gaussian white noise on the $d$-dimensional torus has paths in the Besov spaces $B^{-d/2}_{p,\infty}(\mathbb T^d)$ with $p\in [1, \infty)$. 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 $\hat{b}^{-d/p}_{p,\infty}(\mathbb T^d)$. This is shown to be optimal as well.

Authors

• Mark C. VeraarDelft Institute of Applied Mathematics
Delft University of Technology
P.O. Box 5031
2600 GA Delft, The Netherlands
e-mail

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