In this paper, we find that there is no strong and weak relationship between demimartingales and reverse demimartingales through two examples. Based on this fact, we obtain some maximal inequalities for concave Young functions for reverse demimartingales. Furthermore, we discuss the strong law of large numbers and the strong growth rate for reverse demimartingales.

中文翻译：

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基于凹杨函数的最大不等式及反半鞅应用

本文通过两个例子发现半鞅和反半鞅之间不存在强弱关系。基于这一事实，我们获得了反半鞅的凹杨氏函数的一些最大不等式。此外，我们还讨论了强大数定律和反向半鞅的强劲增长率。