Geodesic
Images of Gaussian random fields: Salem sets and interior points
Narn-Rueih Shieh1 ; Yimin Xiao2
1 Department of Mathematics National Taiwan University Taipei 10617, Taiwan
2 Department of Statistics and Probability Michigan State University A-413 Wells Hall East Lansing, MI 48824, U.S.A.
Studia Mathematica, Tome 176 (2006) no. 1, pp. 37-60 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Let $X = \{X(t),\, t \in \mathbb R^N\}$ be a Gaussian random field in $\mathbb R^d$ with stationary increments. For any Borel set $E \subset \mathbb R^N$, 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 \cite{Pitt78} and Kahane \cite{Kahane85a, Kahane85b} for fractional Brownian motion.
DOI : 10.4064/sm176-1-3
Keywords: mathbb gaussian random field mathbb stationary increments borel set subset mathbb provide sufficient conditions image salem set have interior points studying asymptotic properties fourier transform occupation measure continuity local times respectively results extend improve previous theorems pitt cite pitt kahane cite kahane kahane fractional brownian motion

Narn-Rueih Shieh 1 ; Yimin Xiao 2

1 Department of Mathematics National Taiwan University Taipei 10617, Taiwan
2 Department of Statistics and Probability Michigan State University A-413 Wells Hall East Lansing, MI 48824, U.S.A. 
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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, pp. 37-60. doi: 10.4064/sm176-1-3

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