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Branching Brownian motion: almost sure growth along scaled paths. (English) Zbl 1248.60100
Donati-Martin, Catherine (ed.) et al., Séminaire de Probabilités XLIV. Papers based on the presentations at the 44th séminaire de probabilités, Dijon, France, June 2010. Berlin: Springer (ISBN 978-3-642-27460-2/pbk; 978-3-642-27461-9/ebook). Lecture Notes in Mathematics 2046, 375-399 (2012).
Summary: We give a proof of a result on the growth of the number of particles along chosen paths in a branching Brownian motion. The work follows the approach of classical large deviations results, in which paths of particles in \(C[0, T]\), for large \(T\), are rescaled onto \(C[0, 1]\). The methods used are probabilistic and take advantage of modern spine techniques.
For the entire collection see [Zbl 1244.60005].

MSC:
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
60J65 Brownian motion
60F10 Large deviations
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