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November 2017 Lévy processes and Lévy white noise as tempered distributions
Robert C. Dalang, Thomas Humeau
Ann. Probab. 45(6B): 4389-4418 (November 2017). DOI: 10.1214/16-AOP1168

Abstract

We identify a necessary and sufficient condition for a Lévy white noise to be a tempered distribution. More precisely, we show that if the Lévy measure associated with this noise has a positive absolute moment, then the Lévy white noise almost surely takes values in the space of tempered distributions. If the Lévy measure does not have a positive absolute moment of any order, then the event on which the Lévy white noise is a tempered distribution has probability zero.

Citation

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Robert C. Dalang. Thomas Humeau. "Lévy processes and Lévy white noise as tempered distributions." Ann. Probab. 45 (6B) 4389 - 4418, November 2017. https://doi.org/10.1214/16-AOP1168

Information

Received: 1 September 2015; Revised: 1 October 2016; Published: November 2017
First available in Project Euclid: 12 December 2017

zbMATH: 06838123
MathSciNet: MR3737914
Digital Object Identifier: 10.1214/16-AOP1168

Subjects:
Primary: 60G51
Secondary: 60G20 , 60G60 , 60H40

Keywords: Lévy process , Lévy random field , Lévy white noise , positive absolute moment , tempered distribution

Rights: Copyright © 2017 Institute of Mathematical Statistics

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Vol.45 • No. 6B • November 2017
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