Regularity of Gaussian white noise on the d-dimensional torus

@article{MarkC2011,
abstract = {In this paper we prove that a Gaussian white noise on the d-dimensional torus has paths in the Besov spaces $B^\{-d/2\}_\{p,∞\}(^d)$ 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 $b̂^\{-d/p\}_\{p,∞\}(^d)$. This is shown to be optimal as well.},
author = {Mark C. Veraar},
journal = {Banach Center Publications},
keywords = {Gaussian white noise; Gaussian processes; Besov spaces; Sobolev spaces; path regularity; Fourier-Besov spaces},
language = {eng},
number = {1},
pages = {385-398},
title = {Regularity of Gaussian white noise on the d-dimensional torus},
url = {http://eudml.org/doc/281684},
volume = {95},
year = {2011},
}

TY - JOUR
AU - Mark C. Veraar
TI - Regularity of Gaussian white noise on the d-dimensional torus
JO - Banach Center Publications
PY - 2011
VL - 95
IS - 1
SP - 385
EP - 398
AB - In this paper we prove that a Gaussian white noise on the d-dimensional torus has paths in the Besov spaces $B^{-d/2}_{p,∞}(^d)$ 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 $b̂^{-d/p}_{p,∞}(^d)$. This is shown to be optimal as well.
LA - eng
KW - Gaussian white noise; Gaussian processes; Besov spaces; Sobolev spaces; path regularity; Fourier-Besov spaces
UR - http://eudml.org/doc/281684
ER -