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Some Properties of stochastic compactness

Part of: Distribution theory - Probability Stochastic processes Limit theorems

Published online by Cambridge University Press:  09 April 2009

R. A. Maller
R. A. Maller
Affiliation:
CSIRO Division of Mathematics and Statistics, Perth, Western Australia
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Abstract

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The aim of this paper is to show that some of the known properties of distributions in the domain of attraction of a stable law have counterparts for distributions which are stochastically compact in the sense of Feller. This enables us to unify the ideas of Feller and Doeblin, who first studied the concept of stochastic compactness, and give new characterizations of stochastic compactness and the domain of attraction of the normal distribution.

MSC classification

Secondary: 60F05: Central limit and other weak theorems 60E07: Infinitely divisible distributions; stable distributions 60G50: Sums of independent random variables; random walks
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 30 , Issue 3 , February 1981 , pp. 264 - 277
Copyright
Copyright © Australian Mathematical Society 1981

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