Regularisation of cylindrical Lévy processes in Besov spaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916405523251200 |
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| author | Griffiths, Matthew Riedle, Markus |
| author_facet | Griffiths, Matthew Riedle, Markus |
| contents | In this work, we quantify the irregularity of a given cylindrical Lévy process $L$ in $L^2({\mathbb R}^d)$ by determining the range of weighted Besov spaces $B$ in which $L$ has a regularised version $Y$, that is a stochastic process $Y$ in the classical sense with values in $B$. Our approach is based on characterising Lévy measures on Besov spaces. As a by-product, we determine those Besov spaces $B$ for which the embedding of $L^2({\mathbb R}^d)$ into $B$ is $0$-Radonifying and $p$-Radonifying for $p>1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_13880 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Regularisation of cylindrical Lévy processes in Besov spaces Griffiths, Matthew Riedle, Markus Probability 60G20, 47B10, 60H25, 60G51, 60E07 In this work, we quantify the irregularity of a given cylindrical Lévy process $L$ in $L^2({\mathbb R}^d)$ by determining the range of weighted Besov spaces $B$ in which $L$ has a regularised version $Y$, that is a stochastic process $Y$ in the classical sense with values in $B$. Our approach is based on characterising Lévy measures on Besov spaces. As a by-product, we determine those Besov spaces $B$ for which the embedding of $L^2({\mathbb R}^d)$ into $B$ is $0$-Radonifying and $p$-Radonifying for $p>1$. |
| title | Regularisation of cylindrical Lévy processes in Besov spaces |
| topic | Probability 60G20, 47B10, 60H25, 60G51, 60E07 |
| url | https://arxiv.org/abs/2409.13880 |