Images of Gaussian random fields: Salem sets and interior points

Narn-Rueih Shieh, and Yimin Xiao. "Images of Gaussian random fields: Salem sets and interior points." Studia Mathematica 176.1 (2006): 37-60. <http://eudml.org/doc/284400>.

@article{Narn2006,
abstract = {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.},
author = {Narn-Rueih Shieh, Yimin Xiao},
journal = {Studia Mathematica},
keywords = {fractional Brownian motion; fractional Riesz-Bessel motion; Hausdorff dimension; Fourier dimension; local times},
language = {eng},
number = {1},
pages = {37-60},
title = {Images of Gaussian random fields: Salem sets and interior points},
url = {http://eudml.org/doc/284400},
volume = {176},
year = {2006},
}

TY - JOUR
AU - Narn-Rueih Shieh
AU - Yimin Xiao
TI - Images of Gaussian random fields: Salem sets and interior points
JO - Studia Mathematica
PY - 2006
VL - 176
IS - 1
SP - 37
EP - 60
AB - 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.
LA - eng
KW - fractional Brownian motion; fractional Riesz-Bessel motion; Hausdorff dimension; Fourier dimension; local times
UR - http://eudml.org/doc/284400
ER -