We study an ergodic singular control problem with constraint of a regular one-dimensional linear diffusion. The constraint allows the agent to control the diffusion only at the jump times of an independent Poisson process. Under relatively weak assumptions, we characterize the optimal solution as an impulse-type control policy, where it is optimal to exert the exact amount of control needed to push the process to a unique threshold. Moreover, we discuss the connection of the present problem to ergodic singular control problems, and illustrate the results with different well-known cost and diffusion structures.

中文翻译：

---

随机干预时间的扩散遍历控制

我们研究了具有规则一维线性扩散约束的遍历奇异控制问题。该约束允许代理仅在独立泊松过程的跳跃时间控制扩散。在相对较弱的假设下，我们将最优解决方案描述为一种脉冲型控制策略，在这种策略中，施加将过程推到唯一阈值所需的确切控制量是最优的。此外，我们讨论了当前问题与遍历奇异控制问题的联系，并用不同的众所周知的成本和扩散结构来说明结果。