Regularity of Gaussian white noise on the d-dimensional torus

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

2010-10-29

arxiv.org/abs/1010.6219v2

Mathematics

Probability

Scientific paper

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

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