Limit theorems for the left random walk on GLd(R)

被引：14

作者：

Cuny, Christophe ^{[1
]}

Dedecker, Jerome ^{[2
]}

Jan, Christophe ^{[3
]}

机构：

[1] Cent Supelec, Lab MICS, F-92295 Chatenay Malabry, France

[2] Univ Paris 05, Sorbonne Paris Cite, Lab MAP5, UMR 8145, 45 Rue St Peres, F-75270 Paris 06, France

[3] Lycee Claude Fauriel, Ave Liberat, F-42000 St Etienne, France

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2017年 / 53卷 / 04期

关键词：

Central Limit theorem; Random walks on GLd (R); Strong invariance principles; STATIONARY-PROCESSES; MARTINGALE DIFFERENCES; INVARIANCE-PRINCIPLES; CONVERGENCE-RATES; RANDOM-VARIABLES; RANDOM MATRICES; MARKOV-CHAINS; LARGE NUMBERS; PARTIAL-SUMS; SEQUENCES;

D O I：

10.1214/16-AIHP773

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 a recent work of Benoist and Quint and extending results from the PhD thesis of the third author, we obtain limit theorems for products of independent and identically distributed elements of GLd (R), such as the Marcinkiewicz-Zygmund strong law of large numbers, the CLT (with rates in Wasserstein's distances) and almost sure invariance principles with rates.

引用

页码：1839 / 1865

页数：27

共 27 条

[1] CONVERGENCE-RATES IN THE LAW OF LARGE NUMBERS FOR MARTINGALES [J].

ALSMEYER, G .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1990, 36 (02) :181-194

[2]

Benoist Y., QUINT RANDOM WALKS R

[3] CENTRAL LIMIT THEOREM FOR LINEAR GROUPS [J].

Benoist, Yves ;

Quint, Jean-Francois .

ANNALS OF PROBABILITY, 2016, 44 (02) :1308-1340

[4] KOMLOS-MAJOR-TUSNADY APPROXIMATION UNDER DEPENDENCE [J].

Berkes, Istvan ;

Liu, Weidong ;

Wu, Wei Biao .

ANNALS OF PROBABILITY, 2014, 42 (02) :794-817

[5]

Bougerol P., 1985, Progress in Probability and Statistics, V8

[6]

Cuny C., 2016, ANN PROBAB IN PRESS

[7] Strong Invariance Principles with Rate for "Reverse" Martingale Differences and Applications [J].

Cuny, Christophe ;

Merlevede, Florence .

JOURNAL OF THEORETICAL PROBABILITY, 2015, 28 (01) :137-183

[8] A compact LIL for martingales in 2-smooth Banach spaces with applications [J].

Cuny, Christophe .

BERNOULLI, 2015, 21 (01) :374-400

[9] On the functional central limit theorem for stationary processes [J].

Dedecker, J ;

Rio, E .

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2000, 36 (01) :1-34

[10] Rates of convergence in the strong invariance principle under projective criteria [J].

Dedecker, Jerome ;

Doukhan, Paul ;

Merlevede, Florence .

ELECTRONIC JOURNAL OF PROBABILITY, 2012, 17 :1-31

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