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Quasi-sure analysis on Ito's Wiener space
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UNSPECIFIED (1995) Quasi-sure analysis on Ito's Wiener space. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 321 (12). pp. 1609-1614. ISSN 0764-4442.
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Abstract
We show that one can always linearly embed an abstract Wiener space (E, H, m) into the corresponding Ito's Wiener space (Omega, H, gamma), where Omega consists of all the linear (but not necessarily continuous) functionals on H, such that the family of all gamma-regular measures on Omega is 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 of Omega. The family of all Malliavin T'-fields on E is exactly the family of all the restrictions to E of Malliavin T-r-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 viceversa.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Journal or Publication Title: | COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE | ||||
Publisher: | GAUTHIER-VILLARS | ||||
ISSN: | 0764-4442 | ||||
Official Date: | 14 December 1995 | ||||
Dates: |
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Volume: | 321 | ||||
Number: | 12 | ||||
Number of Pages: | 6 | ||||
Page Range: | pp. 1609-1614 | ||||
Publication Status: | Published |
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