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| GIRSANOV'S THEOREM ON ABSTRACT WIENER SPACES |
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Citation： |
Zhang Yinnan.GIRSANOV'S THEOREM ON ABSTRACT WIENER SPACES[J].Chinese Annals of Mathematics B,1997,18(1):35~46 |
| Page view： 1068
Net amount： 766 |
Authors： |
Zhang Yinnan; |
Foundation： |
Project supported by the National Natural Science
Foundation of China |
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| Abstract： |
Let $(E,H,\mu )$ be an abstract Wiener space
in the sense of L. Gross. It is proved that if $u$ is a
measurable map from $E$ to $H$ such that $u\in {W}^{2.1}(H,\mu
)$ and there
exists a constant $\alpha$, $0<\alpha <1$, such that either $\sum\limits_
n\|D_nu(w)\|_H^2\le\alpha^2$ a.s. or
$\|u(w+h)-u(w)\|_H\le \alpha \|h\|_H$ a. s. for every $h\in H$
and $ E\Big(\text{exp}\Big(\frac{108}{(1-\alpha)^2}\Big(\sum\|D_n u
\|_H)\Big)\Big)\Big)<\infty,$
then the measure $\mu\circ T^{-1}$ is equivalent to $\mu$, where $
T(w)=w+u(w)$ for $w\in E$. And the explicit expression of the Radon-Nikodym
derivative (cf. Theorem 2.1) is given. |
Keywords： |
Gaussian measure, Wiener space, Measurable map |
Classification： |
60B05 |
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