Diffusion arrêtée au premier instant où l'amplitude atteint un niveau donné

The amplitude of a real process X, is the increasing process A defined as the difference between its maximum process and its minimum process. We study the Brownian case, and we characterize, in particular, the law of the first time when A reaches a fixed level a ≷0. We apply this basic study to the case when X is a continuous diffusion and also when X is the angular part of a planar Brownian motion