TY - JOUR
T1 - Limit theorems for functionals of linear processes in critical regions
AU - Xiong, Yudan
AU - Xu, Fangjun
AU - Yu, Jinjiong
N1 - Publisher Copyright:
© 2025 Elsevier B.V.
PY - 2026/1
Y1 - 2026/1
N2 - Let X={Xn:n∈N} be the linear process defined by Xn=∑j=1∞ajɛn−j, where the coefficients aj=j−βℓ(j) are constants with β>0 and ℓ a slowly varying function, and the innovations {ɛn}n∈Z are i.i.d. random variables belonging to the domain of attraction of an α-stable law with α∈(0,2]. Limit theorems for the partial sum S[Nt]=∑n=1[Nt][K(Xn)−EK(Xn)] with proper measurable functions K have been extensively studied, except for two critical regions: I. α∈(1,2),β=1 and II. αβ=2,β≥1. In this paper, we address these open scenarios and identify the asymptotic distributions of S[Nt] under mild conditions.
AB - Let X={Xn:n∈N} be the linear process defined by Xn=∑j=1∞ajɛn−j, where the coefficients aj=j−βℓ(j) are constants with β>0 and ℓ a slowly varying function, and the innovations {ɛn}n∈Z are i.i.d. random variables belonging to the domain of attraction of an α-stable law with α∈(0,2]. Limit theorems for the partial sum S[Nt]=∑n=1[Nt][K(Xn)−EK(Xn)] with proper measurable functions K have been extensively studied, except for two critical regions: I. α∈(1,2),β=1 and II. αβ=2,β≥1. In this paper, we address these open scenarios and identify the asymptotic distributions of S[Nt] under mild conditions.
KW - Domain of attraction of stable law
KW - Limit theorem
KW - Linear process
KW - Long/short memory
UR - https://www.scopus.com/pages/publications/105017618822
U2 - 10.1016/j.spa.2025.104784
DO - 10.1016/j.spa.2025.104784
M3 - 文章
AN - SCOPUS:105017618822
SN - 0304-4149
VL - 191
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
M1 - 104784
ER -