Generalized random fields and L\'evy's continuity theorem on the space of tempered distributions

Hermine Bierm\'e; Olivier Durieu; Yizao Wang

Generalized random fields and L\'evy's continuity theorem on the space of tempered distributions

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arxiv 1706.09326 v1 pith:CPLTB5MJ submitted 2017-06-28 math.PR

Hermine Biermé , Olivier Durieu , Yizao Wang This is my paper · ORCID

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keywords fieldsgeneralizedrandomtheoremcontinuitydistributionsnoteproof

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In this note, we recall main properties of generalized random fields and present a proof of the continuity theorem of Paul L\'evy for generalized random fields in the space of tempered distributions. This theorem was first proved by Fernique (1968) in a more general setting. The aim of this note is to provide a self-contained proof that in particular avoids the abstract theory of nuclear spaces.

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