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June, 2004 Hausdorff dimension of the graph of the Fractional Brownian Sheet
Antoine Ayache
Rev. Mat. Iberoamericana 20(2): 395-412 (June, 2004).


Let $\{B^{(\alpha)}(t)\}_{t\in\mathbb{R}^{d}}$ be the Fractional Brownian Sheet with multi-index $\alpha=(\alpha_1,\ldots, \alpha_d)$, $0< \alpha_i< 1$. In \cite{Kamont1996}, Kamont has shown that, with probability $1$, the box dimension of the graph of a trajectory of this Gaussian field, over a non-degenerate cube $Q\subset\mathbb{R}^{d}$ is equal to $d+1-\min(\alpha_1,\ldots,\alpha_d)$. In this paper, we prove that this result remains true when the box dimension is replaced by the Hausdorff dimension or the packing dimension.


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Antoine Ayache. "Hausdorff dimension of the graph of the Fractional Brownian Sheet." Rev. Mat. Iberoamericana 20 (2) 395 - 412, June, 2004.


Published: June, 2004
First available in Project Euclid: 17 June 2004

zbMATH: 1057.60033
MathSciNet: MR2073125

Primary: 60G15 , 60G17 , 60G60
Secondary: ‎42C40 , 60G50

Keywords: fractional Brownian motion , Gaussian fields , Hausdorff dimension , Packing dimension , random wavelet series

Rights: Copyright © 2004 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.20 • No. 2 • June, 2004
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