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Question regarding Ito representation theorem

Let $H$ be a Gaussian Hilbert space and $H^{:n:}$ be the homogeneous chaos of order $n$. and let $D_n:=\{(t_1,\cdots,t_n):t_1<t_2<\cdots <t_n\}$. … Hence by writting down the chaos decomposition of $X$ and by linearity of the stochastic integral we have that $X$ can be written as a stochastic integral of some square integrable predictable process. …
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