family of random variables such that $\mathbf{E}\left( B(\varphi) B(\psi) \right)  =
\langle\varphi, \psi\rangle_{{\mathcal{H}}}$. Denote by $I_{n}$ the multiple stochastic integral with respect to $B$ (see [@N]). This $I_{n}$ is actually an isometry between the Hilbert space ${\mathcal{H}}^{\odot n}$(symmetric tensor product) equipped with the scaled norm $\frac{1}{\sqrt{n!}}\Vert\cdot\Vert_{{\mathcal{H}}^{\otimes n}}$ and the Wiener chaos of order $n$ which is defined as the closed linear span of the random variables $H_{n}(B(\varphi))$ where $\varphi\in{\mathcal{H}}, \Vert\varphi\Vert_{{\mathcal{H}}}=1$ and $H_{n}$ is the Hermite polynomial of degree $n\geq 1$ $$H_{n}(x)=\frac{(-1)^{n}}{n!} \exp \left( \frac{x^{2}}{2} \right)
\frac{d^{n}}{dx^{n}}\left( \exp \left( -\frac{x^{2}}{2}\right)
\right), \hskip0.5cm x\in \mathbb{R}.$$ The isometry of multiple integrals can be written as: for $m,n$ positive integers, $$\begin{aligned}
\mathbf{E}\left(I_{n}(f) I_{m}(g) \right) &=& n! \langle f,g\rangle _{{\mathcal{H}}^{\otimes n}}\quad \mbox{if } m=n,\nonumber \\
\mathbf{E}\left(I_{n}(f) I_{m}(g) \right) &= & 0\quad \mbox{if } m\not=n.\label{iso}\end{aligned}$$ It also holds that $$I_{n}(f) = I_{n}\big( \tilde{f}\big)$$ where $\tilde{f} $ denotes the symmetrization of $f$ defined by $\tilde{f}(x_{1}, \ldots , x_{x}) =\frac{1}{n!} \sum_{\sigma \in {\cal S}_{n}}
f(x_{\sigma (1) }, \ldots , x_{\sigma (n) } ) $.

We recall that any square integrable random variable which is measurable with respect to the $\sigma$-algebra generated by $B$ can be expanded into an orthogonal sum of multiple stochastic integrals $$\label{sum1} F=\sum_{n\geq0}I_{n}(f_{n})$$ where $f_{n}\in{\mathcal{H}}^{\odot 