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