Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
Wiener and Cameron-Martin space; space of sequences; Fourier series
Wiener and Cameron-Martin space; space of sequences; Fourier series
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.
References:
[1] Bogachev V. I.: Gaussian measures on linear spaces. Analysis 8, J. Maths. Sci. 79, no. 2 (1996), 933–1034. MR 1393507 | Zbl 0881.28009
[2] Gross L.: Abstract Wiener measure. Lecture Notes in Math. 140 (1970), Springer-Verlag. MR 0265548 | Zbl 0203.13002
[3] Ikeda N., Watanabe S.: Stochastic Differential Equations and Diffusion Processes. 2nd edition (1989), North-Holland Publishing Company. MR 1011252 | Zbl 0684.60040
[4] Katznelson Y.: An Introduction to Harmonic Analysis. Dover Publications (1976). MR 0422992 | Zbl 0352.43001
[5] Kuo H. H. : Gaussian measures in Banach spaces. Lecture Notes in Math. 463 (1975) , Springer-Verlag. MR 0461643 | Zbl 0306.28010
[6] Nualart D.: Malliavin Calculus and Related Topics. Springer-Verlag 1996.
[7] Revuz D., Yor M.: Continuous Martingales and Brownian Motion. Springer-Verlag 1991. MR 1083357 | Zbl 0731.60002
[8] Watanabe S.: Lectures on Stochastic Differential Equations and Malliavin Calculus. Tata Inst. Fundamental Research (1984), Springer-Verlag. MR 0742628 | Zbl 0546.60054
Search
Partner of
