It is shown that there is a close relationship between the convergence of a sequence of normalized Galton-Watson processes and the convergence of the rowsums of a certain triangular array of independent identically distributed random variables. Using this result some limit theorems by Jirina and Lamperti are strengthened.
Publié le : 1974-12-14
Classification:
Galton-Watson processes,
weak convergence in $D \lbrack 0,1 \rbrack$,
diffusion approximation,
60J80,
60F05,
60J60
@article{1176996496,
author = {Grimvall, Anders},
title = {On the Convergence of Sequences of Branching Processes},
journal = {Ann. Probab.},
volume = {2},
number = {6},
year = {1974},
pages = { 1027-1045},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996496}
}
Grimvall, Anders. On the Convergence of Sequences of Branching Processes. Ann. Probab., Tome 2 (1974) no. 6, pp. 1027-1045. http://gdmltest.u-ga.fr/item/1176996496/