Sur l'indépendance d'un temps d'arrêt T et de la position BT d'un mouvement brownien (Bu,u⩾0)

Abstract

In this Note, we describe many examples of two-dimensional random variables {B_T,T} obtained from the position of a Brownian motion $\text{(B}{}_{\mathrm{t}}\text{;}\text{t⩾0)}$ at a stopping time T such that T and B_T are independent. For such pairs, the law of T determines that of B_T and vice versa; we study the constraints on these laws induced by the independence assumption.