SIAM Journal on Control and Optimization, Volume 58, Issue 6, Page 3363-3388, January 2020.
Linear formulations for the occupation measures of a diffusion process with singular boundary behavior and an arbitrary but fixed control process are motivated and derived. Under specific assumptions on the control process, the existence and uniqueness of solutions to these linear formulations for both long-term average or discounted cost criteria in infinite time are shown. In particular, absolute continuity for the occupation measure of the nonsingular behavior is proven. Two examples of simple Brownian diffusion illustrate the applicability of the results on specific control problems, and their relevance for ongoing research in stochastic control is discussed.

中文翻译：

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基于奇异随机控制问题的无限维线性问题的解结构

SIAM控制与优化杂志，第58卷，第6期，第3363-3388页，2020年1月
。激发并推导了具有奇异边界行为的扩散过程和任意但固定的控制过程的占线度量。在控制过程的特定假设下，显示了这些线性公式在无限时间内的长期平均或折价成本标准的解决方案的存在和唯一性。特别是，证明了非奇异行为占用度量的绝对连续性。简单布朗扩散的两个例子说明了该结果在特定控制问题上的适用性，并讨论了它们与正在进行的随机控制研究的相关性。