Images of Gaussian random fields: Salem sets and interior points

• Autorzy: Narn-Rueih Shieh , Yimin Xiao
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 60G15: Gaussian processes
• 60G60: Random fields
• 42B10: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
• 28A80: Fractals
• 43A46: Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)
• 60G17: Sample path properties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2006
• Tom: 176
• Numer: 1
• Strony: 37-60

Daty

wydano

2006

Twórcy

autor

Narn-Rueih Shieh

• Department of Mathematics, National Taiwan University, Taipei 10617, Taiwan

autor

Yimin Xiao

• Department of Statistics and Probability, Michigan State University, A-413 Wells Hall, East Lansing, MI 48824, U.S.A.

Identyfikatory

DOI

10.4064/sm176-1-3