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Regularity of Gaussian white noise on the d-dimensional torus

Mark C. Veraar — 2011

Banach Center Publications

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

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