Wiener integral in the space of sequences of real numbers
de Andrade, Alexandre ; Ruffino, Paulo R. C.
Archivum Mathematicum, Tome 036 (2000), p. 95-101 / Harvested from Czech Digital Mathematics Library

Let $i:H\rightarrow W$ be the canonical Wiener space where $W$={$\sigma :[0,T]\rightarrow {R}$ continuous with $\sigma \left( 0\right) =0\rbrace $, $H$ is the Cameron-Martin space and $i$ is the inclusion. We lift a isometry $H\rightarrow l_{2}$ to a linear isomorphism $\Phi :W\rightarrow {\cal V}\subset {R}^{\infty }$ which pushes forward the Wiener structure into the abstract Wiener space (AWS) $i:l_{2}\rightarrow {\cal V}$. Properties of the Wiener integration in this AWS are studied.

Publié le : 2000-01-01
Classification:  46G12,  60B11,  60H05,  60H07
@article{107722,
     author = {Alexandre de Andrade and Paulo R. C. Ruffino},
     title = {Wiener integral in the space of sequences of real numbers},
     journal = {Archivum Mathematicum},
     volume = {036},
     year = {2000},
     pages = {95-101},
     zbl = {1045.60003},
     mrnumber = {1761614},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107722}
}
de Andrade, Alexandre; Ruffino, Paulo R. C. Wiener integral in the space of sequences of real numbers. Archivum Mathematicum, Tome 036 (2000) pp. 95-101. http://gdmltest.u-ga.fr/item/107722/

Bogachev V. I. Gaussian measures on linear spaces, Analysis 8, J. Maths. Sci. 79, no. 2 (1996), 933–1034. (1996) | MR 1393507 | Zbl 0881.28009

Gross L. Abstract Wiener measure, Lecture Notes in Math. 140 (1970), Springer-Verlag. (1970) | MR 0265548 | Zbl 0203.13002

Ikeda N.; Watanabe S. Stochastic Differential Equations and Diffusion Processes, 2nd edition (1989), North-Holland Publishing Company. (1989) | MR 1011252 | Zbl 0684.60040

Katznelson Y. An Introduction to Harmonic Analysis, Dover Publications (1976). (1976) | MR 0422992 | Zbl 0352.43001

Kuo H. H. Gaussian measures in Banach spaces, Lecture Notes in Math. 463 (1975) , Springer-Verlag. (1975) | MR 0461643 | Zbl 0306.28010

Nualart D. Malliavin Calculus and Related Topics, Springer-Verlag 1996. (1996)

Revuz D.; Yor M. Continuous Martingales and Brownian Motion, Springer-Verlag 1991. (1991) | MR 1083357 | Zbl 0731.60002

Watanabe S. Lectures on Stochastic Differential Equations and Malliavin Calculus, Tata Inst. Fundamental Research (1984), Springer-Verlag. (1984) | MR 0742628 | Zbl 0546.60054