CONVERGENCE THEOREMS AND MAXIMAL INEQUALITIES FOR MARTINGALE ERGODIC PROCESSES

doi:10.1016/S0252-9602(10)60123-3

数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (4): 1269-1279.doi: 10.1016/S0252-9602(10)60123-3

CONVERGENCE THEOREMS AND MAXIMAL INEQUALITIES FOR MARTINGALE ERGODIC PROCESSES

罗光洲¹, 马璇^2*, 刘培德³

1. School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China;2. College of Sciences, Huazhong Agricultural University, |Wuhan 430070, China|3. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

收稿日期:2007-12-26 修回日期:2008-10-17 出版日期:2010-07-20 发布日期:2010-07-20
通讯作者: 马璇

CONVERGENCE THEOREMS AND MAXIMAL INEQUALITIES FOR MARTINGALE ERGODIC PROCESSES

LUO Guang-Zhou¹, MA Xuan^2*, LIU Pei-De³

1. School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China;2. College of Sciences, Huazhong Agricultural University, |Wuhan 430070, China|3. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

Received:2007-12-26 Revised:2008-10-17 Online:2010-07-20 Published:2010-07-20
Contact: MA Xuan

摘要/Abstract

摘要：

In this article, we study two types of martingale ergodic processes. We prove that a.e. convergence and L^p 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.

关键词: Ergodic theory, martingale, convergence, maximal inequalities

Abstract:

Key words: Ergodic theory, martingale, convergence, maximal inequalities

中图分类号:

37A30

罗光洲, 马璇, 刘培德. CONVERGENCE THEOREMS AND MAXIMAL INEQUALITIES FOR MARTINGALE ERGODIC PROCESSES[J]. 数学物理学报(英文版), 2010, 30(4): 1269-1279.

LUO Guang-Zhou, MA Xuan, LIU Pei-De. CONVERGENCE THEOREMS AND MAXIMAL INEQUALITIES FOR MARTINGALE ERGODIC PROCESSES[J]. Acta mathematica scientia,Series B, 2010, 30(4): 1269-1279.

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CONVERGENCE THEOREMS AND MAXIMAL INEQUALITIES FOR MARTINGALE ERGODIC PROCESSES

CONVERGENCE THEOREMS AND MAXIMAL INEQUALITIES FOR MARTINGALE ERGODIC PROCESSES

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