| Title:
|
Wiener integral in the space of sequences of real numbers (English) |
| Author:
|
de Andrade, Alexandre |
| Author:
|
Ruffino, Paulo R. C. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
36 |
| Issue:
|
2 |
| Year:
|
2000 |
| Pages:
|
95-101 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Wiener and Cameron-Martin space |
| Keyword:
|
space of sequences |
| Keyword:
|
Fourier series |
| MSC:
|
46G12 |
| MSC:
|
60B11 |
| MSC:
|
60H05 |
| MSC:
|
60H07 |
| idZBL:
|
Zbl 1045.60003 |
| idMR:
|
MR1761614 |
| . |
| Date available:
|
2008-06-06T22:25:23Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107722 |
| . |
| Reference:
|
[1] Bogachev V. I.: Gaussian measures on linear spaces.Analysis 8, J. Maths. Sci. 79, no. 2 (1996), 933–1034. Zbl 0881.28009, MR 1393507 |
| Reference:
|
[2] Gross L.: Abstract Wiener measure.Lecture Notes in Math. 140 (1970), Springer-Verlag. Zbl 0203.13002, MR 0265548 |
| Reference:
|
[3] Ikeda N., Watanabe S.: Stochastic Differential Equations and Diffusion Processes.2nd edition (1989), North-Holland Publishing Company. Zbl 0684.60040, MR 1011252 |
| Reference:
|
[4] Katznelson Y.: An Introduction to Harmonic Analysis.Dover Publications (1976). Zbl 0352.43001, MR 0422992 |
| Reference:
|
[5] Kuo H. H. : Gaussian measures in Banach spaces.Lecture Notes in Math. 463 (1975) , Springer-Verlag. Zbl 0306.28010, MR 0461643 |
| Reference:
|
[6] Nualart D.: Malliavin Calculus and Related Topics.Springer-Verlag 1996. |
| Reference:
|
[7] Revuz D., Yor M.: Continuous Martingales and Brownian Motion.Springer-Verlag 1991. Zbl 0731.60002, MR 1083357 |
| Reference:
|
[8] Watanabe S.: Lectures on Stochastic Differential Equations and Malliavin Calculus.Tata Inst. Fundamental Research (1984), Springer-Verlag. Zbl 0546.60054, MR 0742628 |
| . |
