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Pré-Publication, Document De Travail Année : 2017

Generalized random fields and Lévy's continuity Theorem on the space of tempered distributions

Résumé

In this note, we recall main properties of generalized random fields and present a proof of the continuity theorem of Paul Lévy for generalized random fields in the space of tempered distributions. This theorem was first proved by Fernique 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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Dates et versions

hal-01568486 , version 1 (25-07-2017)

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  • HAL Id : hal-01568486 , version 1

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Hermine Biermé, Olivier Durieu, Yizao Wang. Generalized random fields and Lévy's continuity Theorem on the space of tempered distributions. 2017. ⟨hal-01568486⟩
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