The unscaled paths of branching brownian motion

Simon C. Harris; Matthew I. Roberts

Annales de l'I.H.P. Probabilités et statistiques (2012)

  • Volume: 48, Issue: 2, page 579-608
  • ISSN: 0246-0203

Abstract

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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.

How to cite

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Harris, Simon C., and Roberts, Matthew I.. "The unscaled paths of branching brownian motion." Annales de l'I.H.P. Probabilités et statistiques 48.2 (2012): 579-608. <http://eudml.org/doc/272013>.

@article{Harris2012,
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.},
author = {Harris, Simon C., Roberts, Matthew I.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {branching brownian motion; large deviations; survival probability; law of large numbers; branching Brownian motion},
language = {eng},
number = {2},
pages = {579-608},
publisher = {Gauthier-Villars},
title = {The unscaled paths of branching brownian motion},
url = {http://eudml.org/doc/272013},
volume = {48},
year = {2012},
}

TY - JOUR
AU - Harris, Simon C.
AU - Roberts, Matthew I.
TI - The unscaled paths of branching brownian motion
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2012
PB - Gauthier-Villars
VL - 48
IS - 2
SP - 579
EP - 608
AB - 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.
LA - eng
KW - branching brownian motion; large deviations; survival probability; law of large numbers; branching Brownian motion
UR - http://eudml.org/doc/272013
ER -

References

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