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

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.