Abstract
Every measurable real-valued function $f$ on the space of Wiener process paths with $E(|f|^p) < \infty$ (where $0 < p < 1$) can be represented as a stochastic integral $f = \int \varphi dX$, where $E(\int \varphi^2(t)dt)^{p/2} < \infty$. A similar result holds for $1 < p < \infty$ if and only if $E(f) = 0$.
Citation
D. J. H. Garling. "The Range of Stochastic Integration." Ann. Probab. 6 (2) 332 - 334, April, 1978. https://doi.org/10.1214/aop/1176995578
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