2010/01/14 by Simon C. Harris, Harris, Simon C., Matthew I. Roberts +1
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #60J80 #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR #msc:60J80
paper · pdf · doi:10.48550/arxiv.1001.2471
34 pages, 1 figure. Strengthened Theorem 3
openalex publication_date 2010/01/14 · arxiv created 2010/09/23 · arxiv updated 2010/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a set A⊂ C[0,∞), we give new results on the growth of the number of particles in a dyadic branching Brownian motion whose paths fall within A. We show that it is possible to work without rescaling the paths. We give large deviations probabilities as well as a more sophisticated proof of a result on growth in the number of particles along certain sets of paths. Our results reveal that the number of particles can oscillate dramatically. As a byproduct of our methods we also obtain new results on the number of particles near the frontier of the model. The methods used are entirely probabilistic.