I've got trouble finding the convergence of the following series. Let's first assume that: $$ \lim_{n\rightarrow \infty} \theta_{0}^{n} = 0$$ The series I've got trouble finding the convergence of is: $$\frac{1}{nT} vec\bigg[ \sum_{t=1}^{T} (I \otimes\theta_{0}^{t} y_{i0})\Omega (I\otimes y_{i0}^{'}\theta_{0}^{'t})\bigg]$$
Where $ y_{i0}^{'}$ simply is the transpose of $y_{i0}$.
Any help would really be appreciated.
Thanks,