Denseness of certain smooth Lévy functionals in $\DD_{1,2}$
| dc.creator | Geiss, Christel | |
| dc.creator | Laukkarinen, Eija | |
| dc.date | 2008-05-30 | |
| dc.date.accessioned | 2026-07-07T09:41:51Z | |
| dc.date.available | 2026-07-07T09:41:51Z | |
| dc.description | The Malliavin derivative for a Lévy process $(X_t)$ can be defined on the space $\DD_{1,2}$ using a chaos expansion or in the case of a pure jump process also via an increment quotient operator \cite{sole-utzet-vives}. In this paper we define the Malliavin derivative operator $\D$ on the class $\mathcal{S}$ of smooth random variables $f(X_{t_1}, ..., X_{t_n}),$ where $f$ is a smooth function with compact support. We show that the closure of $L_2(\Om) \supseteq \mathcal{S} \stackrel{\D}{\to} L_2(\m\otimes \mass)$ yields to the space $\DD_{1,2}.$ As an application we conclude that Lipschitz functions map from $\DD_{1,2}$ into $\DD_{1,2}.$ | |
| dc.description | 16 pages | |
| dc.identifier | https://arxiv.org/abs/0805.4704 | |
| dc.identifier | http://arxiv.org/abs/0805.4704 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/161977 | |
| dc.subject | Probability | |
| dc.subject | 60H07; 60G51 | |
| dc.title | Denseness of certain smooth Lévy functionals in $\DD_{1,2}$ | |
| dc.type | text |