Abstract :
[en] The aim of this paper is to prove that wavelet leaders allow to get very fine properties of the trajectories of the Brownian motion: more precisely, we show that there exist (at least) three different behaviors for the size of wavelet leaders of the Brownian motion. Furthermore, they correspond to the three well-known behaviors of its oscillations, namely to be ordinary, rapid and slow. Some links between the oscillations and the size of wavelet leaders at a given point are also given.
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