Images of Gaussian random fields: Salem sets and interior points
Studia Mathematica, Tome 176 (2006) no. 1, p. 37.

Voir la notice de l'article dans European Digital Mathematics Library

Let X = X ( t ) , t ∈ ℝ N be a Gaussian random field in ℝ d with stationary increments. For any Borel set E ⊂ ℝ N , we provide sufficient conditions for the image X(E) to be a Salem set or to have interior points by studying the asymptotic properties of the Fourier transform of the occupation measure of X and the continuity of the local times of X on E, respectively. Our results extend and improve the previous theorems of Pitt [24] and Kahane [12,13] for fractional Brownian motion.
Classification : 60G15, 60G17, 60G60, 43A46, 42B10, 28A80
Mots-clés : fractional Brownian motion, fractional Riesz-Bessel motion, Hausdorff dimension, Fourier dimension, local times 
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Narn-Rueih Shieh; Yimin Xiao. Images of Gaussian random fields: Salem sets and interior points. Studia Mathematica, Tome 176 (2006) no. 1, p. 37. https://geodesic-test.mathdoc.fr/item/STUMA_2006__176_1_284400/