Wiener空间上恒等式自适应扰动可逆的充分条件
Sufficient Conditions for the Invertibility of Adapted Perturbations of Identity on the Wiener Space
摘要：
设$(W,H,μ)$为经典Wiener空间。假设$U=I_W+u$是身份的适应扰动，即，$u:W\to H$适用于$W$的规范过滤。给出了$u$的一些充分的解析条件，这些条件暗示了$U$的可逆性。特别是它表明，如果$u\in \DD_{p,1}(H)$是适应，如果$\exp({1/2}\|\nabla u\|_2^2-δu)\in L^q(μ)$，其中$p^{-1}+q^{-1}=1$，那么$I_W+u$几乎肯定是可逆的。因此，如果存在整数$k\geq 1$使得$\|\nabla^k u\|_{H^{\otimes(k+1)}}\in L^\infty(μ)$，则$I_W+u$又几乎必然可逆。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
