## The Annals of Probability

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

### Uniform Local Behavior of Stable Subordinators

#### 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

**Permanent link to this document**

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**

links.jstor.org

**Subjects**

Primary: 60J30

**Keywords**

Stable subordinator sample function behavior Galton-Watson process

#### Citation

Fristedt, Bert. Uniform Local Behavior of Stable Subordinators. Ann. Probab. 7 (1979), no. 6, 1003--1013. doi:10.1214/aop/1176994893. https://projecteuclid.org/euclid.aop/1176994893