Planning a cost‐efficient monitoring policy of stochastic processes arises from many industrial problems. We formulate a simple discrete‐time monitoring problem of continuous‐time stochastic processes with its applications to several industrial problems. A key in our model is a doubling trick of the variables, with which we can construct an algorithm to solve the problem. The cost‐efficient monitoring policy balancing between the observation cost and information loss is governed by an optimality equation of a fixed point type, which is solvable with an iterative algorithm based on the Feynman‐Kac formula. This is a new linkage between monitoring problems and mathematical sciences. We show regularity results of the optimization problem and present a numerical algorithm for its approximation. A problem having model ambiguity is presented as well. The presented model is applied to problems of environment, ecology, and energy, having qualitatively different target stochastic processes with each other.

中文翻译：

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基于离散观测的连续时间随机过程的经济高效监控

规划随机过程的一种经济高效的监视策略是由许多工业问题引起的。我们提出了一个连续时间随机过程的简单离散时间监控问题，并将其应用于一些工业问题。模型中的关键是变量加倍，通过它我们可以构造算法来解决问题。观测成本与信息损失之间的经济高效的监控策略平衡由定点类型的最优方程控制，该方程可通过基于Feynman-Kac公式的迭代算法求解。这是监控问题和数学科学之间的新联系。我们显示了优化问题的规律性结果，并给出了其逼近的数值算法。还提出了具有模型模糊性的问题。