Invariance of Malliavin fields on Ito's Wiener space and on abstract Wiener space
UNSPECIFIED (1996) Invariance of Malliavin fields on Ito's Wiener space and on abstract Wiener space. JOURNAL OF FUNCTIONAL ANALYSIS, 138 (2). pp. 449-476. ISSN 0022-1236Full text not available from this repository.
Let (E, H, m) be an abstract Wiener space and (Omega, H, gamma) be the corresponding Ito's Wiener space where Omega consists of all the linear (but not necessarily continuous) functionals on the Hilbert space H. We show that one can always linearly embed (E, H, m) into (Omega, H, gamma) in such a way that the family of all gamma-regular measures on Omega are exactly the family of the extensions of all probability measures of finite energy on E. A subset A of E is a slim set if and only if it is a M-null set in Omega. The family of all Malliavin T'-fields on E are exactly the family of all the restrictions of Malliavin T'-fields on Omega. Moreover, the one to one mapping between Malliavin fields on Omega and those on E is commutable with the gradient operator and keeps the Sobolev norms invariant. Hence most of the results of Malliavin calculus known for abstract Wiener space can be transferred to the Ito's Wiener space and vice versa. (C) 1996 Academic Press, Inc.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics|
|Journal or Publication Title:||JOURNAL OF FUNCTIONAL ANALYSIS|
|Publisher:||ACADEMIC PRESS INC JNL-COMP SUBSCRIPTIONS|
|Date:||15 June 1996|
|Number of Pages:||28|
|Page Range:||pp. 449-476|
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