Wiener Integral in the Space of Sequences of Real numbers

Alexandre de Andrade and Paulo R. C. Ruffino

E-mail: ruffino@ime.unicamp.br

Abstract. Let $i:H\rightarrow W$ be the canonical Wiener space where $W$=\{$% \sigma :[0,T]\rightarrow {\Bbb R}$ continuous with $\sigma \left( 0\right) =0\}$, $H$ is the Cameron-Martin space and $i$ is the inclusion. We lift a isometry $H\rightarrow l_{2}$ to a linear isomorphism $\Phi :W\rightarrow {\cal V}\subset {\Bbb R}^{\infty }$ 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.

AMSclassification. 60H07 (60H05, 46S50)

Keywords. Wiener and Cameron-Martin space, space of sequences, Fourier series