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A conceptual approach to a path result for branching Brownian motion. (English) Zbl 1114.60065
Continuing their spine approach to branching diffusions [http:///www.bath.ac.uk/\(^\sim\)massch/ Research/Papers] the authors give an intuitive, fairly straightforward proof of a path large-deviation result for branching Brownian motions with local space-independent binary branching. In contrast to the proof of T.-Y. Lee [Ann. Probab. 20, No. 3, 1288–1309 (1992; Zbl 0759.60024)], which relied on Freidlin’s work on rescaling solutions of reaction-diffusion equations, it combines a spine change of measure with Schilder’s classical large-deviation result for Brownian motion.

MSC:
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
60F10 Large deviations
60J55 Local time and additive functionals
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