Quantum stochatic integrals and Doob-Meyer decomposition
| dc.creator | Luczak, Andrzej | |
| dc.date | 2006-02-10 | |
| dc.date.accessioned | 2026-07-07T07:03:17Z | |
| dc.date.available | 2026-07-07T07:03:17Z | |
| dc.description | We show that for a quantum $L^p$-martingale $(X(t))$, $p>2$, there exists a Doob-Meyer decomposition of the submartingale $(|X(t)|^2)$. A noncommutative counterpart of a classical process continuous with probability one is introduced, and a quantum stochastic integral of such a process with respect to an $L^p$-martingale, $p>2$, is constructed. Using this construction, the uniqueness of the Doob-Meyer decomposition for a quantum martingale `continuous with probability one' is proved, and explicit forms of this decomposition and the quadratic variation process for such a martingale are obtained. | |
| dc.description | 34 pages | |
| dc.identifier | https://arxiv.org/abs/math/0602216 | |
| dc.identifier | http://arxiv.org/abs/math/0602216 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/108916 | |
| dc.subject | Operator Algebras | |
| dc.subject | Probability | |
| dc.subject | Primary: 81S25; Secondary: 46L53 | |
| dc.title | Quantum stochatic integrals and Doob-Meyer decomposition | |
| dc.type | text |