We investigate the x log x condition for a general (Crump–Mode–Jagers) multi-type branching process with a general type space by constructing a size-biased population measure that relates to the ordinary population measure via an intrinsic martingale Wt. Sufficiency of the x log x condition for a non-degenerate limit of Wt is proved and conditions for necessity are investigated.
Publié le : 2009-11-15
Classification:
general branching process,
immigration,
size-biased measure,
xlogx condition
@article{1262962236,
author = {Olofsson, Peter},
title = {Size-biased branching population measures and the multi-type x log x condition},
journal = {Bernoulli},
volume = {15},
number = {1},
year = {2009},
pages = { 1287-1304},
language = {en},
url = {http://dml.mathdoc.fr/item/1262962236}
}
Olofsson, Peter. Size-biased branching population measures and the multi-type x log x condition. Bernoulli, Tome 15 (2009) no. 1, pp. 1287-1304. http://gdmltest.u-ga.fr/item/1262962236/