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VOL. 5 | 2009 Stochastic compactness of Lévy processes
Ross Maller, David M. Mason

Editor(s) Christian Houdré, Vladimir Koltchinskii, David M. Mason, Magda Peligrad

Abstract

We characterize stochastic compactness and convergence in distribution of a Lévy process at “large times", i.e., as t→∞, by properties of its associated Lévy measure, using a mechanism for transferring between discrete (random walk) and continuous time results. We thereby obtain also domain of attraction characterisations for the process at large times. As an illustration of the stochastic compactness ideas, semi-stable laws are considered.

Information

Published: 1 January 2009
First available in Project Euclid: 2 February 2010

zbMATH: 1243.60024
MathSciNet: MR2797951

Digital Object Identifier: 10.1214/09-IMSCOLL516

Subjects:
Primary: 62E17 , 62E20
Secondary: 60F15

Keywords: centered Feller class , domain of attraction , Feller class , Infinitely divisible , large times , Lévy processes

Rights: Copyright © 2009, Institute of Mathematical Statistics

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