Some prevalent results about strongly monoHolder functions

Abstract : We study the typical behaviour of strongly monoHolder functions from the prevalence point of view. To this end we first prove wavelet-based criteria for strongly monoHolder functions. We then use the notion of prevalence to show that the functions of C(alpha)(R(d)) are almost surely strongly monoHolder with Holder exponent a. Finally, we prove that for any alpha is an element of (0, 1) on a prevalent set of C(alpha)(R(d)) the Hausdorff dimension of the graph is equal to d + 1 - alpha.