  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 \[
\left\{\sum\limits_{n=1}^{[Nt]}\big[K(X_n)-\E K(X_n)\big]:\; t\geq 0\right\} \]
as $N$ tends to infinity, where $[Nt]$ is the integer part of $Nt$ for $t\geq
0$.
