On collisions of Brownian particles
Ichiba, Tomoyuki ; Karatzas, Ioannis
Ann. Appl. Probab., Tome 20 (2010) no. 1, p. 951-977 / Harvested from Project Euclid
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We examine the behavior of n Brownian particles diffusing on the real line with bounded, measurable drift and bounded, piecewise continuous diffusion coefficients that depend on the current configuration of particles. Sufficient conditions are established for the absence and for the presence of triple collisions among the particles. As an application to the Atlas model for equity markets, we study a special construction of such systems of diffusing particles using Brownian motions with reflection on polyhedral domains.
Publié le : 2010-06-15
Classification:  Martingale problem,  triple collision,  effective dimension,  Bessel process,  reflected Brownian motion,  comparison theorem,  Atlas model,  60G17,  60G44,  60G85 
@article{1276867303,
     author = {Ichiba, Tomoyuki and Karatzas, Ioannis},
     title = {On collisions of Brownian particles},
     journal = {Ann. Appl. Probab.},
     volume = {20},
     number = {1},
     year = {2010},
     pages = { 951-977},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1276867303}
}

Ichiba, Tomoyuki; Karatzas, Ioannis. On collisions of Brownian particles. Ann. Appl. Probab., Tome 20 (2010) no. 1, pp.  951-977. http://gdmltest.u-ga.fr/item/1276867303/