In the simplest case, we obtain a general solution to a problem of minimizing an integral of a nondecreasing right continuous stochastic process from zero to some nonnegative random variable tau, under the constraints that for some nonnegative random variable T, tau is between zero and T a.s. and the expected value of tau is some alpha. The nondecreasing process and T are allowed to be dependent. In fact a more general setup involving sigma-finite measures, rather than just probability measures is considered and some consequences for families of stochastic processes are given as special cases. Various applications are provided.

中文翻译：

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最小化受随机约束和一些应用的随机凸函数

在最简单的情况下，我们获得了最小化从零到某个非负随机变量 tau 的非递减右连续随机过程的积分问题的一般解，条件是对于某个非负随机变量 T，tau 在 0 和 T 之间as 和 tau 的预期值是一些 alpha。允许非递减过程和 T 是相关的。事实上，考虑了一个更一般的设置，包括 sigma-finite 测度，而不仅仅是概率测度，并且随机过程族的一些后果作为特殊情况给出。提供各种应用程序。