0 & 0 & 2 & 0\\
0 & 0 & 0 & 0
\end{array}\right),
\left(\begin{array}{cccc}
0 & 0 & 0 & 2\\
0 & 0 & 0 & 0
\end{array}\right),
\right.\\
&\hphantom{=\{}
\left(\begin{array}{cccc}
1 & 1 & 0 & 0\\
0 & 0 & 0 & 0
\end{array}\right),
\left(\begin{array}{cccc}
1 & 0 & 1 & 0\\
0 & 0 & 0 & 0
\end{array}\right),
\left(\begin{array}{cccc}
1 & 0 & 0 & 1\\
0 & 0 & 0 & 0
\end{array}\right),
\left(\begin{array}{cccc}
0 & 1 & 1 & 0\\
0 & 0 & 0 & 0
\end{array}\right),\\
&\left.\hphantom{=\{}
\left(\begin{array}{cccc}
0 & 1 & 0 & 1\\
0 & 0 & 0 & 0
\end{array}\right),
\left(\begin{array}{cccc}
0 & 0 & 1 & 1\\
0 & 0 & 0 & 0
\end{array}\right)
\right\}\end{aligned}$$

hen $q_j=2$ for all $j$, they consist of the following convergences: where $F_n,G_n\in\{M_n,W_n\}$.

As a special case of Theorem \[thm:main\], we can deduce a high-dimensional central limit theorem for multiple Skorohod integrals in hyperrectangles as follows. Let $\mathcal{A}^\mathrm{re}(d)$ be the set of all hyperrectangles in $\mathbb{R}^d$, i.e. $\mathcal{A}^\mathrm{re}(d)$ consists of all sets $A$ of the form $$A=\{z\in\mathbb{R}^d:a_j\leq z^j\leq b_j\text{ for all }j=1,\dots,d\}$$ for some $-\infty\leq a_j\leq b_j\leq\infty$, $j=1,\dots,d$. Taking 