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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 , - 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 , - d / p ( d ) . This is shown to be optimal as well.

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