Weak invariance principles for sums of dependent random functions

被引：38

作者：

Berkes, Istvan ^{[1
]}

Horvath, Lajos ^{[2
]}

Rice, Gregory ^{[2
]}

机构：

[1] Graz Univ Technol, Inst Stat, A-8010 Graz, Austria

[2] Univ Utah, Dept Math, Salt Lake City, UT 84112 USA

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2013年 / 123卷 / 02期

基金：

美国国家科学基金会; 奥地利科学基金会;

关键词：

Variables in Hilbert spaces; m-approximability; Weak convergence; VALUED RANDOM-VARIABLES; CENTRAL-LIMIT-THEOREM; STATIONARY-PROCESSES; MOMENT; SPACE;

D O I：

10.1016/j.spa.2012.10.003

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：

Motivated by problems in functional data analysis, in this paper we prove the weak convergence of normalized partial sums of dependent random functions exhibiting a Bernoulli shift structure. (C) 2012 Elsevier B.V. All rights reserved.

引用

页码：385 / 403

页数：19

共 50 条

[1] On weak invariance principles for sums of dependent random functionals
Jirak, Moritz
STATISTICS & PROBABILITY LETTERS, 2013, 83 (10) : 2291 - 2296
[2] On Weak Invariance Principles for Partial Sums
Jirak, Moritz
JOURNAL OF THEORETICAL PROBABILITY, 2017, 30 (03) : 703 - 728
[3] On Weak Invariance Principles for Partial Sums
Moritz Jirak
Journal of Theoretical Probability, 2017, 30 : 703 - 728
[4] Maximum of partial sums and an invariance principle for a class of weak dependent random variables
Peligrad, M
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1998, 126 (04) : 1181 - 1189
[5] ALMOST SURE INVARIANCE PRINCIPLES FOR SUMS OF WEAKLY DEPENDENT RANDOM-VARIABLES
PHILIPP, W
STOUT, WF
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 21 (06): : A557 - A557
[6] WEAK AND LP-INVARIANCE PRINCIPLES FOR SUMS OF B-VALUED RANDOM-VARIABLES
PHILIPP, W
ANNALS OF PROBABILITY, 1980, 8 (01): : 68 - 82
[7] ALMOST SURE INVARIANCE PRINCIPLES FOR PARTIAL SUMS OF WEAKLY DEPENDENT RANDOM-VARIABLES
PHILIPP, W
STOUT, W
MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 2 (2-16) : 1 - 140
[8] Invariance principles for homogeneous sums of free random variables
Deya, Aurelien
Nourdin, Ivan
BERNOULLI, 2014, 20 (02) : 586 - 603
[9] Quadratic Weyl sums, automorphic functions and invariance principles
Cellarosi, Francesco
Marklof, Jens
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2016, 113 : 775 - 828
[10] STRONG INVARIANCE-PRINCIPLES FOR SUMS OF RANDOM VALUES WITH MULTIINDICES
ZINCHENKO, NM
DOPOVIDI AKADEMII NAUK UKRAINSKOI RSR SERIYA A-FIZIKO-MATEMATICHNI TA TECHNICHNI NAUKI, 1983, (11): : 9 - 11

← 1 2 3 4 5 →