Central limit theorems for nearly long range dependent subordinated linear processes

被引：1

作者：

Wendler, Martin ^{[1
]}

Wu, Wei Biao ^{[2
]}

机构：

[1] Ouo von Guericke Univ Magdeburg, Univ Pl 2, D-39106 Magdeburg, Germany

[2] Univ Chicago, 5747 South Ellis Ave, Chicago, IL 60637 USA

来源：

JOURNAL OF APPLIED PROBABILITY | 2020年 / 57卷 / 02期

关键词：

Central limit theorem; long range dependence; linear processes; power rank; FUNCTIONALS; CONVERGENCE; SUMS;

D O I：

10.1017/jpr.2020.10

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：

The limit behavior of partial sums for short range dependent stationary sequences (with summable autocovariances) and for long range dependent sequences (with autocovariances summing up to infinity) differs in various aspects. We prove central limit theorems for partial sums of subordinated linear processes of arbitrary power rank which are at the border of short and long range dependence.

引用

页码：637 / 656

页数：20

共 21 条

[1] NONCENTRAL LIMIT-THEOREMS AND APPELL POLYNOMIALS [J].

AVRAM, F ;

TAQQU, MS .

ANNALS OF PROBABILITY, 1987, 15 (02) :767-775

[2] Sensitivity of the Hermite rank [J].

Bai, Shuyang ;

Taqqu, Murad S. .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2019, 129 (03) :822-840

[3]

Billingsley P., 2013, CONVERGE PROBAB MEAS

[4]

Bingham N. H., 1989, ENCY MATH APPL, V27

[5] CENTRAL LIMIT-THEOREMS FOR NON-LINEAR FUNCTIONALS OF GAUSSIAN FIELDS [J].

BREUER, P ;

MAJOR, P .

JOURNAL OF MULTIVARIATE ANALYSIS, 1983, 13 (03) :425-441

[6] INTEGRATED FUNCTIONALS OF NORMAL AND FRACTIONAL PROCESSES [J].

Buchmann, Boris ;

Chan, Ngai Hang .

ANNALS OF APPLIED PROBABILITY, 2009, 19 (01) :49-70

[7] MARTINGALE TRANSFORMS [J].

BURKHOLD.DL .

ANNALS OF MATHEMATICAL STATISTICS, 1966, 37 (06) :1494-&

[8] Limit theorems for one and two-dimensional random walks in random scenery [J].

Castell, Fabienne ;

Guillotin-Plantard, Nadine ;

Pene, Francoise .

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2013, 49 (02) :506-528

[9] INVARIANCE PRINCIPLE FOR STATIONARY PROCESSES [J].

DAVYDOV, YA .

THEORY OF PROBILITY AND ITS APPLICATIONS,USSR, 1970, 15 (03) :487-&

[10] NON-CENTRAL LIMIT-THEOREMS FOR NONLINEAR FUNCTIONALS OF GAUSSIAN FIELDS [J].

DOBRUSHIN, RL ;

MAJOR, P .

ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1979, 50 (01) :27-52

← 1 2 3 →