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

被引：0

作者：

Liu, Hui ^{[1
]}

Xiong, Yudan ^{[1
]}

Xu, Fangjun ^{[2
,3
]}

机构：

[1] East China Normal Univ, Sch Stat, Shanghai 200262, Peoples R China

[2] East China Normal Univ, Sch Stat, KLATASDS MOE, Shanghai 200062, Peoples R China

[3] NYU Shanghai, Inst Math Sci, NYU ECNU, Shanghai 200062, Peoples R China

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2024年 / 167卷

基金：

中国国家自然科学基金;

关键词：

Linear process; Long memory; Domain of attraction of stable law; Limit theorem; EMPIRICAL PROCESSES; RANDOM-VARIABLES; MOVING AVERAGES; SUMS;

D O I：

10.1016/j.spa.2023.104237

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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. (c) 2023 Elsevier B.V. All rights reserved.

引用

页数：23

共 50 条

[21] Change-of-variance problem for linear processes with long memory
Lihong Wang
Jinde Wang
[J]. Statistical Papers, 2006, 47 : 279 - 298
[22] Central limit theorems for long range dependent spatial linear processes
Lahiri, S. N.
Robinson, Peter M.
[J]. BERNOULLI, 2016, 22 (01) : 345 - 375
[23] New Central Limit Theorems for Functionals of Gaussian Processes and their Applications
José Manuel Corcuera
[J]. Methodology and Computing in Applied Probability, 2012, 14 : 477 - 500
[24] LOCAL LIMIT-THEOREMS FOR FUNCTIONALS OF RANDOM-PROCESSES
DAVYDOV, YA
[J]. THEORY OF PROBABILITY AND ITS APPLICATIONS, 1988, 33 (04) : 732 - 738
[25] Limit theorems for integral functionals of Hermite-driven processes
Garino, Valentin
Nourdin, Ivan
Nualart, David
Salamat, Majid
[J]. BERNOULLI, 2021, 27 (03) : 1764 - 1788
[26] LOCAL LIMIT-THEOREMS FOR FUNCTIONALS OF GAUSSIAN-PROCESSES
DAVYDOV, YA
[J]. THEORY OF PROBABILITY AND ITS APPLICATIONS, 1982, 26 (04) : 856 - 857
[27] New Central Limit Theorems for Functionals of Gaussian Processes and their Applications
Manuel Corcuera, Jose
[J]. METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY, 2012, 14 (03) : 477 - 500
[28] Diagnostic checking in linear processes with infinite variance
Krämer, W
Runde, R
[J]. MATHEMATICAL AND COMPUTER MODELLING, 2001, 34 (9-11) : 1123 - 1131
[29] LINEAR PREDICTION OF ARMA PROCESSES WITH INFINITE VARIANCE
CLINE, DBH
BROCKWELL, PJ
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1985, 19 (02) : 281 - 296
[30] SOME LIMIT THEOREMS ON DISTRIBUTION OF FUNCTIONALS OF PROCESSES ASYMPTOTICALLY APPROACHING MARKOFFS PROCESSES
BOROVKOV, AA
[J]. DOKLADY AKADEMII NAUK SSSR, 1966, 169 (03): : 507 - &

← 1 2 3 4 5 →