Generalized random fields and L\'evy's continuity theorem on the space of tempered distributions
| Autor: | Biermé, Hermine, Durieu, Olivier, Wang, Yizao |
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| Rok vydání: | 2017 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 18 pages |
| Databáze: | arXiv |
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