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December, 1979 Uniform Local Behavior of Stable Subordinators
Bert Fristedt
Ann. Probab. 7(6): 1003-1013 (December, 1979). DOI: 10.1214/aop/1176994893

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.

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Bert Fristedt. "Uniform Local Behavior of Stable Subordinators." Ann. Probab. 7 (6) 1003 - 1013, December, 1979. https://doi.org/10.1214/aop/1176994893

Information

Published: December, 1979
First available in Project Euclid: 19 April 2007

zbMATH: 0438.60060
MathSciNet: MR548894
Digital Object Identifier: 10.1214/aop/1176994893

Subjects:
Primary: 60J30

Rights: Copyright © 1979 Institute of Mathematical Statistics

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Vol.7 • No. 6 • December, 1979
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