Lévy measures on Banach spaces
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916450109751296 |
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| author | van Neerven, Jan Riedle, Markus |
| author_facet | van Neerven, Jan Riedle, Markus |
| contents | We establish an explicit characterisation of Lévy measures on both $L^p$-spaces and UMD Banach spaces. In the case of $L^p$-spaces, Lévy measures are characterised by an integrability condition, which directly generalises the known description of Lévy measures on sequence spaces. The latter has been the only known description of Lévy measures on infinite dimensional Banach spaces that are not Hilbert. Lévy measures on UMD Banach spaces are characterised by the finiteness of the expectation of a random γ-radonifying norm. Although this description is more abstract, it reduces to simple integrability conditions in the case of $L^p$-spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_09362 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lévy measures on Banach spaces van Neerven, Jan Riedle, Markus Functional Analysis Probability Primary: 60B05, Secondary: 46B09, 60E05 60G57, 60H05 We establish an explicit characterisation of Lévy measures on both $L^p$-spaces and UMD Banach spaces. In the case of $L^p$-spaces, Lévy measures are characterised by an integrability condition, which directly generalises the known description of Lévy measures on sequence spaces. The latter has been the only known description of Lévy measures on infinite dimensional Banach spaces that are not Hilbert. Lévy measures on UMD Banach spaces are characterised by the finiteness of the expectation of a random γ-radonifying norm. Although this description is more abstract, it reduces to simple integrability conditions in the case of $L^p$-spaces. |
| title | Lévy measures on Banach spaces |
| topic | Functional Analysis Probability Primary: 60B05, Secondary: 46B09, 60E05 60G57, 60H05 |
| url | https://arxiv.org/abs/2406.09362 |