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Images of Gaussian random fields: Salem sets and interior points

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Shieh N.-R., Xiao Y.

Studia Mathematica

2006

tom 176

nr 1

37-60

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.

Ograniczanie wyników

1 Studia Mathematica

1 Shieh N.-R.

1 Xiao Y.

1 2006

Wyniki wyszukiwania

Images of Gaussian random fields: Salem sets and interior points