Malliavin Calculus and Skorohod Integration for Quantum Stochastic Processes
| dc.creator | Franz, Uwe | |
| dc.creator | Leandre, Remi | |
| dc.creator | Schott, Rene | |
| dc.date | 2000-04-13 | |
| dc.date.accessioned | 2026-07-07T06:42:21Z | |
| dc.date.available | 2026-07-07T06:42:21Z | |
| dc.description | A derivation operator and a divergence operator are defined on the algebra of bounded operators on the symmetric Fock space over the complexification of a real Hilbert space $\eufrak{h}$ and it is shown that they satisfy similar properties as the derivation and divergence operator on the Wiener space over $\eufrak{h}$. The derivation operator is then used to give sufficient conditions for the existence of smooth Wigner densities for pairs of operators satisfying the canonical commutation relations. For $\eufrak{h}=L^2(\mathbb{R}_+)$, the divergence operator is shown to coincide with the Hudson-Parthasarathy quantum stochastic integral for adapted integrable processes and with the non-causal quantum stochastic integrals defined by Lindsay and Belavkin for integrable processes. | |
| dc.description | 28 pages, amsart style | |
| dc.identifier | https://arxiv.org/abs/math/0004088 | |
| dc.identifier | http://arxiv.org/abs/math/0004088 | |
| dc.identifier | Infinite Dimensional Analysis, Quantum Probability and Related Topics, Vol. 4, No. 1 (2001) 11-38 | |
| dc.identifier | doi:10.1142/S0219025701000371 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/102009 | |
| dc.subject | Probability | |
| dc.subject | 81S25; 60H07; 60G15 | |
| dc.title | Malliavin Calculus and Skorohod Integration for Quantum Stochastic Processes | |
| dc.type | text |