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The unscaled paths of branching Brownian motion
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Harris, Simon C. and Roberts, Matthew Iain (2012) The unscaled paths of branching Brownian motion. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, Vol.48 (No.2). pp. 579-608. doi:10.1214/11-AIHP417 ISSN 0246-0203.
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Official URL: http://dx.doi.org/10.1214/11-AIHP417
Abstract
For a set A ⊂ C[0, ∞), we give new results on the growth of the number of particles in a 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. We also obtain new results on the number of particles near the frontier of the model. The methods used are entirely probabilistic.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Journal or Publication Title: | Annales de l'Institut Henri Poincaré, Probabilités et Statistiques | ||||
Publisher: | Institute of Mathematical Statistics | ||||
ISSN: | 0246-0203 | ||||
Official Date: | 2012 | ||||
Dates: |
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Volume: | Vol.48 | ||||
Number: | No.2 | ||||
Page Range: | pp. 579-608 | ||||
DOI: | 10.1214/11-AIHP417 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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