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On multiplicative excessive functions of a branching Brownian motion. (English) Zbl 0668.60074

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.
Reviewer: P.Salminen

MSC:

60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
60J65 Brownian motion
60J60 Diffusion processes
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