its canonical inner product, that is to say $$\langle f, g\rangle_\h:=\int_0^Tf(s) \cdot g(s)ds = \sum_{i=1}^d \int_0^Tf^i(s) g^i(s) ds,\ (f,g)\in \h^2.$$ Let now $H$ be the Cameron-Martin space that is the space of functions in $\Omega$ which are absolutely continuous with square-integrable derivative and which start from $0$ at $0$: $$H:=\left\{ h:[0,T] \longrightarrow {\mathbb{R}}^d, \; \exists \dot{h}\in\h, \; h(t)=\int_0^t \dot{h}(x)dx, \; \forall t\in [0,T]\right\},$$ For any $h$ in $H$, we will always denote by $\dot{h}$ a version of its Radon-Nykodym density with respect to the Lebesgue measure. Then, $H$ is an Hilbert space equipped with the inner product $\langle h_1,h_2 \rangle_{H}:=\langle \dot{h_1},\dot{h_2} \rangle_{\h}$, for any $(h_1, h_2)\in H\times H$, and with associated norm $\|h\|_H^2:=\langle \dot h, \dot h \rangle_\h$. Define next $L^p(\Kc)$ as the set of all $\mathcal F_T$-measurable random variables $F$ which are valued in an Hilbert space $\mathcal{K}$, and such that ${\left\|F\right\|}_{L^p(\Kc)}^p<+\infty$, where $${\left\|F\right\|}_{L^p(\Kc)}:=\left(\E\left[{\left\|F\right\|}_{\mathcal{K}}^p\right]\right)^{1/p}.$$

Let now $\mathcal{S}$ be the set of cylindrical functionals, that is the set of $\mathbb R$-valued random variables $F$ of the form $$\label{eq:cylindrical}
F=f(W(h_1),\ldots,W(h_n)), \quad (h_1,\ldots,h_n) \in H^n, \; f \in C^\infty_b({\mathbb{R}}^n), \text{ for some }n\geq 1,$$ where $W(h):=\int_0^T \dot{h}_s\cdot  dW_s:= \sum_{i=1}^d \int_0^T \dot{h}_s^{i} dW_s^{i}$ for any $h$ in $H$ and where $C^\infty_b({\mathbb{R}}^n)$ denotes the 