Branching Brownian Motion: Almost Sure Growth Along Unscaled Paths
نویسندگان
چکیده
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 [11], Kyprianou [8], and Hardy & Harris [4].
منابع مشابه
Branching Brownian Motion: Almost Sure Growth Along Scaled Paths
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 in C[0, 1] are rescaled onto C[0, T ] for large T . The methods used are probabilistic and take advantage of modern spine techniques.
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