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arXiv.org e-Print Archive
Preprint . 2015
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L\'evy Processes and L\'evy White Noise as Tempered Distributions

descriptionPublicationkeyboard_double_arrow_right Preprint 17 Sep 2015
Authors: Dalang, Robert C.; Humeau, Thomas;

arXiv: 1509.05274

L\'evy Processes and L\'evy White Noise as Tempered Distributions

Abstract

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

Comment: 27 pages

Keywords

Primary 60G51, Secondary 60G60, 60G20, 60H40, Mathematics - Probability

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
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Average
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