Appropriate constant multiples of the function $t^{1/\alpha}$ are "the" "maximal local lower envelope" and "the" "minimal local upper envelope" for the sample functions of a strictly stable subordinator of index $\alpha$. The fact that the probability of extinction of a Galton-Watson process is less than one if the mean number of offspring is larger than one is used in the proofs.
Publié le : 1979-12-14
Classification:
Stable subordinator,
sample function behavior,
Galton-Watson process,
60J30
@article{1176994893,
author = {Fristedt, Bert},
title = {Uniform Local Behavior of Stable Subordinators},
journal = {Ann. Probab.},
volume = {7},
number = {6},
year = {1979},
pages = { 1003-1013},
language = {en},
url = {http://dml.mathdoc.fr/item/1176994893}
}
Fristedt, Bert. Uniform Local Behavior of Stable Subordinators. Ann. Probab., Tome 7 (1979) no. 6, pp. 1003-1013. http://gdmltest.u-ga.fr/item/1176994893/