关于N-弱鞅和弱鞅不等式的一个注记  

A NOTE ON THE INEQUALITIES FOR N-DEMIMARTINGALES AND DEMIMARTINGALES

作　　者：胡舒合[1] 杨文志[1] 王学军[1] 沈燕[1] 

机构地区：[1]安徽大学数学科学学院,合肥230039

出　　处：《系统科学与数学》2010年第8期1052-1058,共7页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(10871001;60803059);安徽省高校省级自然科学基金(KJ2010A005);安徽省高校省级优秀青年人才基金(2010SQRL016ZD);安徽大学青年科学研究基金(2009QN011A)资助课题

摘　　要：N-弱鞅(N-demimartingales)是由Christofides引进的.Christofides指出均值为零的负相协(negatively associated)随机变量序列的部分和序列是N-弱鞅.然而,相关文献中引理2.1的证明有错误,这就影响了其文后的结果引理2.2、定理2.1等.在这篇注记中,修正了相关文献中的引理2.1,作为应用,推广了鞅和下鞅的一些结果.The class of N-demimartingales is introduced by Christofides. Christofides points out that a sequence of partial sums of mean zero negatively associated random variables is an example of an N-demimartingale. However, there is one mistake in the proof of Lemma 2.1, which affects the results of Lemma 2.2, Theorem 2.1, etc. in the above cited reference. In this note a corrected version of some results given therein is presented. As applications, some known results for martingales and submartingales are generalized.

关 键 词：弱鞅 弱下鞅 N-弱鞅 N-弱上鞅 负相协随机变量. 

分 类 号：O211.6[理学—概率论与数理统计]