Abstract
Every measurable real-valued function $f$ on the space of Wiener process paths $\{W(t): 0 \leqq t \leqq 1\}$ can be represented as an Ito stochastic integral $\int^1_0 \varphi(t, \omega) dW(t, \omega)$ where $\varphi$ is a nonanticipating functional with $\int^1_0 \varphi(t, \omega)^2dt < \infty$ for almost all $\omega$.
Citation
R. M. Dudley. "Wiener Functionals as Ito Integrals." Ann. Probab. 5 (1) 140 - 141, February, 1977. https://doi.org/10.1214/aop/1176995898
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