CONVERGENCE THEOREMS AND MAXIMAL INEQUALITIES FOR MARTINGALE ERGODIC PROCESSES

被引：0

作者：

罗光洲 ^{[1
]}

马璇 ^{[2
]}

刘培德 ^{[3
]}

机构：

[1] School of Mathematics and Statistics, Hubei Normal University

[2] College of Sciences, Huazhong Agricultural University

[3] School of Mathematics and Statistics, Wuhan University

来源：

ActaMathematicaScientia | 2010年 / 30卷 / 04期

关键词：

Ergodic theory; martingale; convergence; maximal inequalities;

D O I：

暂无

中图分类号：

O178 [不等式及其他];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we study two types of martingale ergodic processes. We prove that a.e. convergence and Lp convergence as well as maximal inequalities, which are established both in ergodic theory and martingale setting, also hold well for these new sequences of random variables. Moreover, the corresponding theorems in the former two areas turn out to be degenerate cases of the martingale ergodic theorems proved here.

引用

页码：1269 / 1279

页数：11

共 15 条

[1]

Distributed cognitions: Psychological and educational considerations. Perkins DN. Cambridge University Press . 1993

[2]

Ergodic Theory. Petersen K. Cambridge University Press . 1983

[3]

Order from Chaos[Russian Translation]. Prigogine I,Stengers I. Progress . 1986

[4]

Martingales and geometry in Banach spaces. Liu P D. Wuhan University Press . 1993

[5]

Krengel,U. Ergodic Theorems . 1985

[6]

Teoria Ergodica. Mane R. IMPA . 1983

[7]

Martingale Spaces and Inequalities. Long Ruilin. Peking University Press . 1993

[8] S.e.r. [P].

澳大利亚专利 :AU2002950931A0 ,2002-09-12

[9]

Selected topics from the metric theory of dynamical systems. Rohlin,V.A. American Mathematical Society Translations . 1966

[10]

Pointwise Inequalities for Ergodic Averages and Reversed Martingales. Goubran,N. Journal of Mathematical Analysis and Applications . 2004

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