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

Hermine Biermé; Olivier Durieu; Yizao Wang

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arXiv · 1706.09326

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

Hermine Biermé·Olivier Durieu·Yizao Wang

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Abstract

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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Hermine Biermé, Olivier Durieu, Yizao Wang. 2017-06-28. Generalized random fields and L\'evy's continuity theorem on the space of tempered distributions. https://arxiv.org/abs/1706.09326

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