线性扩散方程的双侧Poisson控制
Two-sided Poisson control of linear diffusions
摘要：
研究了一类Poisson约束下的一般线性扩散方程的双边最优控制问题：控制只允许在独立Poisson信号过程的到达时刻进行.我们给出了一个弱的和容易验证的充分条件，在此条件下，我们得到了一个准显式的唯一解的扩散的最小r-过度映射的问题。我们还研究了泊松过程的信号强度对解的极限性质的影响。最后，我们用一个明确的例子来说明我们的结果。
英文摘要：
We study a class of two-sided optimal control problems of general linear diffusions under a so-called Poisson constraint: the controlling is only allowed at the arrival times of an independent Poisson signal processes. We give a weak and easily verifiable set of sufficient conditions under which we derive a quasi-explicit unique solution to the problem in terms of the minimal r-excessive mappings of the diffusion. We also investigate limiting properties of the solutions with respect to the signal intensity of the Poisson process. Lastly, we illustrate our results with an explicit example.
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