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

被引：1

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 18 条

[1] Aaronson J, 1998, ANN PROBAB, V26, P399
[2] Astrauskas J., 1983, LITH MATH J, V23, P127, DOI DOI 10.1007/BF00966355
[3] Functional Convergence of Linear Processes with Heavy-Tailed Innovations
Balan, Raluca
Jakubowski, Adam
Louhichi, Sana
[J]. JOURNAL OF THEORETICAL PROBABILITY, 2016, 29 (02) : 491 - 526
[4] Billingsley, 1999, CONVERGENCE PROBABIL, DOI 10.1002/9780470316962
[5] Breiman L., 1992, Probability, VVolume 7, P421, DOI [10.1137/1.9781611971286, DOI 10.1137/1.9781611971286]
[6] Dudley R.M., 2002, REAL ANAL PROBABILIT
[7] Durrett R., 2010, Probability: theory and examples, DOI 10.1017/CBO9780511779398
[8] Honda T., 2009, Probab. Math. Stat., V29, P337
[9] On the asymptotic distributions of partial, sums of functionals of infinite-variance moving averages
Hsing, T
[J]. ANNALS OF PROBABILITY, 1999, 27 (03) : 1579 - 1599
[10] Ibragimov I. A., 1971, Independent and stationary sequences of random variables

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