A Limit Theorem for Some Linear Processes with Innovations in the Domain of Attraction of a Stable Law

Let X={Xn:n∈N} be a linear process in which the coefficients are of the form ai=i-1ℓ(i) with ℓ 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 α-stable law with α∈(1,2]. We will establish the asymptotic behavior of the partial sum process (Formula presented.) as N tends to infinity, where [t] is the integer part of the nonnegative number t.