Limit theorems for functionals of long memory linear processes with infinite variance

Let $X=\{X_n:n\in \mathbb{N}\}$ be a long memory linear process in which the coefficients are regularly varying and innovations are independent and identically distributed and belong to the domain of attraction of an $\alpha$-stable law with $\alpha \in (0,2)$. Then, for any integrable and square integrable function $K$ on $\mathbb{R}$, under certain mild conditions, we establish the asymptotic behavior of the partial sum process $$\left\{\sum _{n=1}^{[Nt]}\right[K(X_n)-\text{E}K(X_n)]:t\ge 0\}$$ as $N$ tends to infinity, where $[Nt]$ is the integer part of $Nt$ for $t\ge 0$.