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

作者：Liu, Hui; Xiong, Yudan; Xu, Fangjun^*

来源：Stochastic Processes and their Applications, 2024, 167: 104237.

DOI：10.1016/j.spa.2023.104237

• Linear process
• Long memory
• Domain of attraction of stable law
• Limit theorem

Let X = {X-n : n is an element of 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 is an element of (0, 2). Then, for any integrable and square integrable function K on R, under certain mild conditions, we establish the asymptotic behavior of the partial sum process @@@ {Sigma([Nt])(n=1) [K(X-n) - E K(X-n)] : t >= 0} @@@ as N tends to infinity, where [Nt] is the integer part of Nt for t >= 0.