## The Annals of Probability

### Uniform Local Behavior of Stable Subordinators

Bert Fristedt

#### Abstract

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.

#### Article information

Source
Ann. Probab., Volume 7, Number 6 (1979), 1003-1013.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176994893

Digital Object Identifier
doi:10.1214/aop/1176994893

Mathematical Reviews number (MathSciNet)
MR548894

Zentralblatt MATH identifier
0438.60060

JSTOR