P. Vallois, ON THE JOINT LAWS OF MAXIMUM AND TERMINAL VALUE OF SOME CONTINUOUS SUBMARTINGALES, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 317(7), 1993, pp. 693-696
We characterize the joint laws of (X(infinity)BAR, X(infinity)) (resp.
the laws of X(infinity)BAR), X running over the set of positive, cont
inuous and uniformly integrable submartingales X vanishing at 0, where
X(infinity)BAR = max X(t). t greater-than-or-equal-to 0