Sufficient conditions for the existence of a limiting distribution for a multitype branching process with immigration in a random environment, $Z(t)$, are given. In the case when the environment is an independent, identically distributed sequence, sufficient conditions are given which insure that the tail of the distribution of $\nu = \inf\{t > 0: Z(t) = 0\}$ decreases exponentially fast, and an application of this fact to random walk in a random environment is indicated.
Publié le : 1987-01-14
Classification:
Multitype branching process with immigration in a random environment,
limiting distributions,
regeneration times,
products of random matrices,
random walk in a random environment,
60J10,
60J15
@article{1176992273,
author = {Key, Eric S.},
title = {Limiting Distributions and Regeneration Times for Multitype Branching Processes with Immigration in a Random Environment},
journal = {Ann. Probab.},
volume = {15},
number = {4},
year = {1987},
pages = { 344-353},
language = {en},
url = {http://dml.mathdoc.fr/item/1176992273}
}
Key, Eric S. Limiting Distributions and Regeneration Times for Multitype Branching Processes with Immigration in a Random Environment. Ann. Probab., Tome 15 (1987) no. 4, pp. 344-353. http://gdmltest.u-ga.fr/item/1176992273/