Martingale Central Limit Theorem for Triangular Array Martingale Difference Sequence I was wondering if anyone out there would know of an appropriate central limit theorem (or be able to apply a central limit theorem type argument) that would allow me to find an asymptotic distribution/weak convergence of the following Martingale Difference Sequence (MDS):
Let $\left\{\xi_j^n\right\}_{j=1}^n \sim $ MDS $(0,\sigma^4)$. Then:
\begin{equation*}
\frac{1}{\sqrt{n}}\sum_{j=1}^n \xi_j^n \quad \overset{\mathcal{D}}\longrightarrow \quad ??
\end{equation*}
By the ....??.... theorem under ...?... (some assumptions), as $n\rightarrow\infty$? 
I now this is not a very "well posed" problem per se, and if there are any other "assumptions" that are required/needed in order to obtain this sort of weak convergence please let me know. Also could you also please provide a reference/references so that I may study this in a little bit more depth myself.
Many thanks

You could use the result of McLeish, which is perfectly suited to the setting of arrays of martingale differences.
