Martingale methods have played an important role in the theory of Galton-Watson processes and branching random walks. The (random) Fourier transform of the position of the particles in the $n$th generation, normalized by its mean, is a martingale. Under second moments assumptions on the branching this has been very useful to study the asymptotics of the branching random walk. Using a different normalization, we obtain a new martingale which is in $L^2$ under weak assumptions on the displacement of the particles and strong assumptions on the branching.
Publié le : 1993-11-14
Classification:
Spatial growth in branching random walk,
Banach space valued martingales,
genealogy of Galton-Watson tree,
60J80,
60G42,
60J15
@article{1177005276,
author = {Joffe, A.},
title = {A New Martingale in Branching Random Walk},
journal = {Ann. Appl. Probab.},
volume = {3},
number = {4},
year = {1993},
pages = { 1145-1150},
language = {en},
url = {http://dml.mathdoc.fr/item/1177005276}
}
Joffe, A. A New Martingale in Branching Random Walk. Ann. Appl. Probab., Tome 3 (1993) no. 4, pp. 1145-1150. http://gdmltest.u-ga.fr/item/1177005276/