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| 摘要: |
| 本文研究了鞅差序列的一些不等式.利用条件期望性质和基本不等式，获得了鞅差序列的Bernstein，Kolmogorov和Hoeffding不等式，推广了有界随机向量相应的结果.另外，得到了鞅差序列的最大部分和的经典Kolmogorov和Rosenthal不等式，补充了次线性期望下独立和负相依随机变量的相应结果. |
| 关键词: 鞅差序列 Bernstein不等式 Kolmogorov不等式 Hoeffding不等式 Rosenthal不等式 |
| DOI： |
| 分类号:O211.6;O211.4 |
| 基金项目:Supported by Scientific Program of Department of Education of Jiangxi Province of China (GJJ150894); National Natural Science Foundation of China (61662037). |
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| PROBABILITY INEQUALITIES AND ROSENTHAL INEQUALITIES FOR THE SEQUENCE OF MARTINGALE DIFFERENCES |
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XU Ming-zhou,CHENG Kun,DING Yun-zheng,ZHOU Yong-zheng
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| Abstract: |
| In this paper, we discuss some inequalities for the sequence of martingale differences. By using properties of conditional expectation and elementary inequalities, we obtain the basic inequalities of Bernstein, Kolomogrov, Hoeffding for the sequence of martingale differences, which extend the results on the case of bounded random vectors. Moreover, we obtain classical Kolmogorov and Rosenthal inequalities for maximum partial sums of martingale differences, which complement the results on the case of independent and negatively dependent random variables under sub-linear expectations. |
| Key words: martingale differences Bernstein inequality Kolmogorov inequality Hoeffding inequality Rosenthal inequality |
