The stochastic process is one of the important branches of probability theory which deals with probabilistic models that evolve over time. It starts with probability postulates and includes a captivating arrangement of conclusions from those postulates. In probability theory, a convex function applied on the expected value of a random variable is always bounded above by the expected value of the convex function of that random variable. The purpose of this note is to introduce the class of generalized -convex stochastic processes. Some well-known results of generalized -convex functions such as Hermite-Hadamard, Jensen, and fractional integral inequalities are extended for generalized -stochastic convexity.

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Hermite-Hadamard、Jensen 和广义凸随机过程的分数积分不等式

随机过程是概率论的重要分支之一，它处理随时间演变的概率模型。它从概率假设开始，包括从这些假设中得出的一系列引人入胜的结论。在概率论中，应用于随机变量的期望值的凸函数总是以该随机变量的凸函数的期望值为界。本笔记的目的是介绍一类广义-凸随机过程。广义一些知名结果-凸函数如厄米-哈达玛，詹森，和分数积分不等式延伸广义-随机凸。