On multiplicative excessive functions of a branching Brownian motion (Q1118262)

Stochastic calculus is used to characterize multiplicative excessive functions of a binary branching Brownian motion with a constant creation rate. Some properties of the martingales given by invariant functions are studied. In particular, it is seen that these positive and unbounded martingales tend a.s. to 0 and are not square integrable. Informally speaking, they exhibit a clustering phenomenon in the underlying supercritical branching Brownian motion.