Sufficient Conditions for the Invertibility of Adapted Perturbations of Identity on the Wiener Space
| dc.creator | Ustunel, Ali Suleyman | |
| dc.creator | Zakai, Moshe | |
| dc.date | 2006-05-16 | |
| dc.date | 2006-11-01 | |
| dc.date.accessioned | 2026-07-07T08:07:48Z | |
| dc.date.available | 2026-07-07T08:07:48Z | |
| dc.description | Let $(W,H,μ)$ be the classical Wiener space. Assume that $U=I_W+u$ is an adapted perturbation of identity, i.e., $u:W\to H$ is adapted to the canonical filtration of $W$. We give some sufficient analytic conditions on $u$ which imply the invertibility of the map $U$. In particular it is shown that if $u\in \DD_{p,1}(H)$ is adapted and if $\exp({1/2}\|\nabla u\|_2^2-δu)\in L^q(μ)$, where $p^{-1}+q^{-1}=1$, then $I_W+u$ is almost surely invertible. As a consequence, if, there exists an integer $k\geq 1$ such that $\|\nabla^k u\|_{H^{\otimes(k+1)}}\in L^\infty(μ)$, then $I_W+u$ is again almost surely invertible. | |
| dc.identifier | https://arxiv.org/abs/math/0605433 | |
| dc.identifier | http://arxiv.org/abs/math/0605433 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/131053 | |
| dc.subject | Probability | |
| dc.subject | Functional Analysis | |
| dc.subject | Statistics Theory | |
| dc.subject | 60H07, 60H05, 60H25, 60G15, 60G30, 60G35, 46G12, 47H05, 47H1, 35J60 | |
| dc.title | Sufficient Conditions for the Invertibility of Adapted Perturbations of Identity on the Wiener Space | |
| dc.type | text |