Fractional order Sobolev spaces on Wiener space. (English) Zbl 0792.60049
Fractional order Sobolev spaces are introduced on an abstract Wiener space and Donsker’s delta functions are defined as generalized Wiener functionals belonging to Sobolev spaces with negative differentiability indices. By using these notions, the regularity in the sense of Hölder continuity of a class of conditional expectations is obtained.
Reviewer: S.Watanabe (Kyoto)
MSC:
| 60H07 | Stochastic calculus of variations and the Malliavin calculus |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
Keywords:
fractional order Sobolev spaces; abstract Wiener space; Donsker’s delta functions; generalized Wiener functionals; Hölder continuityReferences:
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