Dimension de Hausdorff du graphe d'une fonction continue : nouvelles majorations déterministes et minorations presque sûres

Abstract

In this Note, we establish an upper bound of the Hausdorff dimension of the graph of a continuous function depending on its wavelet coefficients in a sufficiently regular wavelet basis. In particular, this bound is related to the Besov smoothness of the function. An almost sure lower bound of the same quantity is stated for some precise classes of random functions.