WHEN DOES THE RAMER FORMULA LOOK LIKE THE GIRSANOV FORMULA
成果类型：
Article
署名作者：
ZAKAI, M; ZEITOUNI, O
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1176989698
发表日期：
1992
页码：
1436-1440
关键词：
摘要：
Let {B, H, P0) be an abstract Wiener space and for every real rho, let T(rho)omega = omega + rho-F(omega) be a transformation from B to B. It is well known that under certain assumptions the measures induced by T(rho) or T(rho)-1 are mutually absolutely continuous with respect to P0 and the density function is represented by the Ramer formula. In this formula, the Carleman-Fredholm determinant det2(I(H) + rho-del-F) appears as a factor. We characterize the class of del-F for which a.s.-P0, det2(I(H) + rho-del-F) = 1 for all rho in an open subset of R, in which case the form of Ramer's expression reduces to the familiar Cameron-Martin-Maruyama-Girsanov form. The proof is based on a characterization of quasinilpotent Hilbert-Schmidt operators.