On the Hausdorff dimension of graphs of prevalent continuous functions on compact sets
Résumé
Let $K$ be a compact set in $\rd$ with positive Hausdorff dimension. Using a Fractional Brownian Motion, we prove that in a prevalent set of continuous functions on $K$, the Hausdorff dimension of the graph is equal to $\dim_{\mathcal H}(K)+1$. This is the largest possible value. This result generalizes a previous work due to J.M. Fraser and J.T. Hyde which was exposed in the conference {\it Fractal and Related Fields~2}. The case of $\alpha$-Hölderian functions is also discussed.
Domaines
Analyse classique [math.CA]
Origine : Fichiers produits par l'(les) auteur(s)
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