Enlargement of the Wiener filtration by an absolutely continuous random variable via Malliavin's calculus
成果类型：
Article
署名作者：
Imkeller, P
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s004400050059
发表日期：
1996
页码：
105-135
关键词：
摘要：
The analytic treatment of problems related to the asymptotic behaviour of random dynamical systems generated by stochastic differential equations suffers from the presence of non-adapted random invariant measures. Semimartingale theory becomes accessible if the underlying Wiener filtration is enlarged by the information carried by the orthogonal projectors on the Oseledets spaces of the (linearized) system. We study the corresponding problem of preservation of the semimartingale property and the validity of a priori inequalities between the norms of stochastic integrals in the enlarged filtration and norms of their quadratic variations in case the random element F enlarging the filtration is real valued and possesses an absolutely continuous law. Applying the tools of Malliavin's calculus, we give smoothness conditions on F under which the semimartingale property is preserved and a priori martingale inequalities are valid.
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