Let $\{\mathbf{Z}_n\}$ be a multitype branching process in a random environment (MBPRE) which grows to infinity with positive probability for almost all environmental sequences. Under some conditions involving the first two moments of the environmental sequence, it is shown that dividing the $\{\mathbf{Z}_n\}$ components by their environment-conditioned expectations yields a sequence convergent in $L^2$ to a random vector with equal components.
Publié le : 1989-07-14
Classification:
Branching,
random environment,
multitype,
Furstenberg-Kesten theorem,
martingale,
$L^2$-convergence,
60J80,
60F25
@article{1176991259,
author = {Cohn, Harry},
title = {On the Growth of the Multitype Supercritical Branching Process in a Random Environment},
journal = {Ann. Probab.},
volume = {17},
number = {4},
year = {1989},
pages = { 1118-1123},
language = {en},
url = {http://dml.mathdoc.fr/item/1176991259}
}
Cohn, Harry. On the Growth of the Multitype Supercritical Branching Process in a Random Environment. Ann. Probab., Tome 17 (1989) no. 4, pp. 1118-1123. http://gdmltest.u-ga.fr/item/1176991259/