A necessary and sufficient condition for the invertibility of adapted perturbations of identity on the Wiener space
| dc.creator | Üstünel, Ali Süleyman | |
| dc.date | 2008-09-01 | |
| dc.date.accessioned | 2026-07-07T09:59:44Z | |
| dc.date.available | 2026-07-07T09:59:44Z | |
| dc.description | Let $(W,H,μ)$ be the classical Wiener space, assume that $U=I_W+u$ is an adapted perturbation of identity satisfying the Girsanov identity. Then, $U$ is invertible if and only if the kinetic energy of $u$ is equal to the relative entropy of the measure induced with the action of $U$ on the Wiener measure $μ$, in other words $U$ is invertible if and only if $$ \half \int_W|u|_H^2dμ=\int_W \frac{dUμ}{dμ}\log\frac{dUμ}{dμ}dμ. $$ | |
| dc.identifier | https://arxiv.org/abs/0809.0215 | |
| dc.identifier | http://arxiv.org/abs/0809.0215 | |
| dc.identifier | Comptes Rendus Mathematiques, Vol. 346, 2008 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/168129 | |
| dc.subject | Probability | |
| dc.subject | Functional Analysis | |
| dc.subject | 60Hxx | |
| dc.title | A necessary and sufficient condition for the invertibility of adapted perturbations of identity on the Wiener space | |
| dc.type | text |