Qian Yu

Limit Theorems for Tempered Linear Processes with Innovations in the Domain of Attraction of a Stable Law

We study the partial-sum behavior of tempered linear processes \[ X_{N,n}=\sum_{j=1}^{\infty}e^{-\lambda_Nj}\frac{\ell(j)}{j}\varepsilon_{n-j}, \qquad \lambda_N\downarrow0, \] where $\ell$ is slowly varying and the innovations belong to the domain of attraction of an $\alpha$-stable law with $1<\alpha\leq2$. The filter...