\\   
    & =\lim_{n\to\infty}  \frac{1}{n^{\frac{p+q}{2}-1}} \sum_{k, \ell =0}^{p, q}\binom{p}{k} \binom{q}{\ell} \sum_{m=1}^{ \min \{k,\ell\} } T^m_{k,\ell}, \mbox{ say},\end{aligned}$$ where for each $m=1,2, \ldots, \min\{p,q\}$, $I_m$ is defined as $$\label{def:I_k}
    I_{m}:=\{((i_1,\ldots,i_{k}),(j_1,\ldots,j_{\ell}))\in A_{k}\times A_{\ell}\suchthat |\{i_1,\ldots,i_{k}\}\cap \{j_1,\ldots,j_{\ell}\}|=m\}.$$ Now we calculate the contribution due to the typical term $T^m_{k,\ell}$ of (\[eqn:T\_k,l\_SC\]) for some fixed value of $k= 1, 2, \ldots, p$, $\ell= 1, 2, \ldots, q$ and $m =1,2, \ldots, \min\{k,\ell\}$. Since from (\[eqn:condition\]), we have $$\E[X_i]= 0, \ \E(X^2_i)=1 \mbox{ and } \sup_{i \geq 1}\E(|X_i|^{k})= \alpha_k < \infty \mbox{ for } k \geq 3.$$ Therefore there exist $\gamma >0$, which depends only on $k$ and $\ell$, such that $$\begin{aligned}
 \label{eqn:gamma_1}
%   \sum_{A_{k}, A_{\ell}} \E[ X_0^{p+q-k-\ell}] \E[X_{i_1}\ldots X_{i_{k}}X_{j_1}\ldots X_{j_{\ell}}]-\E[ X_0^{p-k}]\E[ X_0^{q-\ell}]  \E[X_{i_1}\ldots X_{i_{k}}]\E[X_{j_1}\ldots X_{j_{\ell}}]
    |T^m_{k,\ell}| & = \sum_{I_m} |\E[ X_0^{p+q-k-\ell} X_{i_1} \cdots X_{i_{k}} X_{j_1} \cdots X_{j_{\ell}} ] -\E[X_0^{p-k} X_{i_1} \cdots X_{i_{k}} ] \E[X_0^{q-\ell}  X_{j_1} \cdots X_{j_{\ell}} ] | \nonumber \\   
    & \leq \gamma |B_{k,\ell}|,
    \end{aligned}$$ where $B_{k,\ell} \subseteq A_k \times A_\ell$ with conditions that $\{ i_1, i_2,\ldots,i_k \} \cap \{ j_1, j_2,\ldots,j_\ell \} \neq \emptyset$ and each element of set $\{ i_1, i_2,\ldots,i_{k}\} \cup \{ j_1, j_2, \ldots, j_\ell\} $ has multiplicity greater than or equal to two. So, to solve (\[eqn:gamma\_1\]), it is enough to 