This work presents a study of a finite-time horizon stochastic control problem with restrictions on both the reward and the cost functions. To this end, it uses standard dynamic programming techniques, and an extension of the classic Lagrange multipliers approach. The coefficients considered here are supposed to be unbounded, and the obtained strategies are of non-stationary closed-loop type. The driving thread of the paper is a sequence of examples on a pollution accumulation model, which is used for the purpose of showing three algorithms for the purpose of replicating the results. There, the reader can find a result on the interchangeability of limits in a Dirichlet problem.

中文翻译：

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控制污染累积的约束马尔可夫扩散模型

这项工作提出了对有限时间范围随机控制问题的研究，该问题对奖励和成本函数都有限制。为此，它使用标准的动态规划技术，以及经典拉格朗日乘数方法的扩展。这里考虑的系数应该是无界的，得到的策略是非平稳闭环类型的。论文的主线是一系列关于污染累积模型的例子，用于展示三种算法以复制结果。在那里，读者可以找到狄利克雷问题中极限互换性的结果。