Mathematics Subject Classification (1991): 60G44, 60J60, 60H15
Springer Online Journal Archives 1860-2000
Abstract. For a wide class of local martingales (M t ) there is a default function, which is not identically zero only when (M t ) is strictly local, i.e. not a true martingale. This default in the martingale property allows us to characterize the integrability of functions of sup s≤t M s in terms of the integrability of the function itself. We describe some (paradoxical) mean-decreasing local sub-martingales, and the default functions for Bessel processes and radial Ornstein–Uhlenbeck processes in relation to their first hitting and last exit times.
Type of Medium: