Limit theory for a class of non-stationary linear processes with weakly dependent heavy-tailed innovations

For a class of non-stationary linear processes $(X_{n})_{n}$ with weakly dependent heavy-tailed innovations we prove a convergence result for the space-time point processes $N_{n}=\sum_{i=1}^{n}δ_{(i/n, X_{i}/a_{n})}$. Using this result and the continuous mapping theorem we then derive functional co