Research

The unscaled paths of branching Brownian motion


Reference:

Harris, S. C. and Roberts, M. I., 2012. The unscaled paths of branching Brownian motion. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 48 (2), pp. 579-608.

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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.

    Details

    Item Type Articles
    CreatorsHarris, S. C.and Roberts, M. I.
    DOI10.1214/11-AIHP417
    DepartmentsFaculty of Science > Mathematical Sciences
    RefereedYes
    StatusPublished
    ID Code26705

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