Branching Brownian motion: Almost sure growth along unscaled paths

2008/11/11 by Simon C. Harris, Harris, Simon, Matthew I. Roberts +1
Mathematics · Physics and Astronomy · Economics, Econometrics and Finance · #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.0811.1704

Abstract

We give new results on the growth of the number of particles in a dyadic branching Brownian motion which follow within a fixed distance of a path f:[0,∞)→ ℝ. We show that it is possible to count the number of particles without rescaling the paths. Our results reveal that the number of particles along certain paths can oscillate dramatically. The methods used are entirely probabilistic, taking advantage of the spine technique developed by, amongst others, Lyons et al, Kyprianou, and Hardy & Harris.

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