Images of Gaussian random fields: Salem sets and interior points

Narn-Rueih Shieh; Yimin Xiao

Studia Mathematica, Tome 173 (2006), p. 37-60 / Harvested from The Polish Digital Mathematics Library

Résumé

Let $X = X (t), t \in ℝ^{N}$ be a Gaussian random field in $ℝ^{d}$ with stationary increments. For any Borel set $E \subset ℝ^{N}$ , 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.

Publié le : 2006-01-01

Zbl 1105.60023

EUDML-ID : urn:eudml:doc:284400

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     title = {Images of Gaussian random fields: Salem sets and interior points},
     journal = {Studia Mathematica},
     volume = {173},
     year = {2006},
     pages = {37-60},
     zbl = {1105.60023},
     language = {en},
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Narn-Rueih Shieh; Yimin Xiao. Images of Gaussian random fields: Salem sets and interior points. Studia Mathematica, Tome 173 (2006) pp. 37-60. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm176-1-3/