Hausdorff dimension of the graph of the Fractional Brownian Sheet | Zendy

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Hausdorff dimension of the graph of the Fractional Brownian Sheet

Author(s) -

Antoine Ayache

Publication year - 2004

Publication title -

revista matemática iberoamericana

Language(s) - English

Resource type - Journals

eISSN - 2235-0616

pISSN - 0213-2230

DOI - 10.4171/rmi/394

Subject(s) - hausdorff dimension , mathematics , graph , brownian motion , effective dimension , dimension (graph theory) , hausdorff measure , packing dimension , combinatorics , minkowski–bouligand dimension , fractal dimension , mathematical analysis , fractal , statistics

Let {B(t)}t∈R d be the Fractional Brownian Sheet with multiindex α = (α1, . . . , αd), 0 < αi < 1. In [14], 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 ⊂ R d is equal to d + 1 − min(α1, . . . , αd). 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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