Regularisation of cylindrical Lévy processes in Besov spaces Article Swipe
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Matthew Griffiths
,
Markus Riedle
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2409.13880
· OA: W4403752780
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2409.13880
· OA: W4403752780
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 $p>1$.
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