We consider a real-valued branching Brownian motion where particles are killed at rate $\mu$ and split at rate $\lambda \leq \mu$ into two independent offspring particles. The process dies out almost surely, so it reaches some lowest level. We prove a decomposition of the branching Brownian path at its minimum. The post-minimum path is just branching Brownian motion conditioned never to go beneath its initial point. The pre-minimum piece is independent of the post-minimum piece, and has the same law as the post-minimum piece reweighted by a functional of the endpoints of the tree. Applications to branching polymers are discussed.
Publié le : 1992-11-14
Classification:
Branching Brownian motion,
pre-minimum,
post-minimum,
rooted family tree with heights,
rooted branching tree with heights,
branching tree with heights,
tree shape with heights,
branching polymers,
super-Brownian motion,
60J65,
60J85,
60J70
@article{1177005584,
author = {Jansons, Kalvis M. and Rogers, L. C. G.},
title = {Decomposing the Branching Brownian Path},
journal = {Ann. Appl. Probab.},
volume = {2},
number = {4},
year = {1992},
pages = { 973-986},
language = {en},
url = {http://dml.mathdoc.fr/item/1177005584}
}
Jansons, Kalvis M.; Rogers, L. C. G. Decomposing the Branching Brownian Path. Ann. Appl. Probab., Tome 2 (1992) no. 4, pp. 973-986. http://gdmltest.u-ga.fr/item/1177005584/