Universal Malliavin Calculus in Fock and Lévy-Itô Spaces
| dc.creator | Applebaum, David | |
| dc.date | 2008-08-19 | |
| dc.date.accessioned | 2026-07-07T09:57:21Z | |
| dc.date.available | 2026-07-07T09:57:21Z | |
| dc.description | We review and extend Lindsay's work on abstract gradient and divergence operators in Fock space over a general complex Hilbert space. Precise expressions for the domains are given, the $L^2$-equivalence of norms is proved and an abstract version of the Itô-Skorohod isometry is established. We then outline a new proof of Itô's chaos expansion of complex Lévy-Itô space in terms of multiple Wiener-Lévy integrals based on Brownian motion and a compensated Poisson random measure. The duality transform now identifies Lévy-Itô space as a Fock space. We can then easily obtain key properties of the gradient and divergence of a general Lévy process. In particular we establish maximal domains of these operators and obtain the Itô-Skorohod isometry on its maximal domain. | |
| dc.description | Submitted to the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/0808.2593 | |
| dc.identifier | http://arxiv.org/abs/0808.2593 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/167308 | |
| dc.subject | Probability | |
| dc.title | Universal Malliavin Calculus in Fock and Lévy-Itô Spaces | |
| dc.type | text |