Geodesic
Wiener integral in the space of sequences of real numbers
Archivum mathematicum, Tome 36 (2000) no. 2, pp. 95-101 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 46G12, 60B11, 60H05, 60H07
Keywords: Wiener and Cameron-Martin space; space of sequences; Fourier series 
@article{ARM_2000_36_2_a1,
     author = {de Andrade, Alexandre and Ruffino, Paulo R. C.},
     title = {Wiener integral in the space of sequences of real numbers},
     journal = {Archivum mathematicum},
     pages = {95--101},
     year = {2000},
     volume = {36},
     number = {2},
     mrnumber = {1761614},
     zbl = {1045.60003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2000_36_2_a1/}
}
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de Andrade, Alexandre; Ruffino, Paulo R. C. Wiener integral in the space of sequences of real numbers. Archivum mathematicum, Tome 36 (2000) no. 2, pp. 95-101. http://geodesic.mathdoc.fr/item/ARM_2000_36_2_a1/