PATHWISE NONLINEAR FILTERING ON ABSTRACT WIENER-SPACES
成果类型：
Article
署名作者：
ENCHEV, O
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1176989139
发表日期：
1993
页码：
1728-1754
关键词：
摘要：
The nonlinear filtering problem is studied for models where the samples of the signal and the noise are elements of some general abstract Wiener space. The signal is allowed to depend on the noise and the optimal filter is expressed as an explicit functional of the observed sample (trajectory). It is shown that this functional satisfies the Zakai equation. As a n technical tool, a class of shift transformations on the Wiener space is studied and an analog of Cameron-Martin-Girsanov's theorem is obtained.