A limit theorem for some linear processes with innovations in the domain of attraction of a stable law

Abstract: Let $X={X_n: n\in\mathbb{N}}$ be a linear process in which the coefficients are of the form $a_i=i^{-1}\ell(i)$ with $\ell$ being a slowly varying function at the infinity and the innovations are independent and identically distributed random variables belonging to the domain of attraction of an $\alpha$-stable law with $\alpha\in (1, 2]$. We will establish the asymptotic behavior of the partial sum process [ \bigg{\sum\limits_{n=1}^{[Nt]} X_n: t\geq 0\bigg} ] as $N$ tends to infinity, where $[t]$ is the integer part of the non-negative number $t$.