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 0022-1236

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Abstract

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
ISSN:	0022-1236
Date:	15 June 1996
Volume:	138
Number:	2
Number of Pages:	28
Page Range:	pp. 449-476
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/18581

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