Impulse and continuous control of piecewise deterministic Markov processes
Impulse and continuous control of piecewise deterministic Markov processes
复制标题
分段确定性马尔可夫过程的脉冲和连续控制
DOI：
10.1080/17442500008834246
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
R. C.A.B.
中科院分区：
文献类型：
--
作者：
O. Costa;R. C.A.B.
在本文中，我们考虑分段确定性马尔可夫过程（PDP）的跳跃率和跳跃后位置参数的脉冲和连续控制问题。在一篇配套论文中，我们研究了 PDP 的连续控制问题的最优停止，假设最终成本函数仅沿轨迹假设绝对连续。在本文中，我们应用这些结果来根据一组拟变分不等式以及过程的第一个跳跃时间算子来获得 PDP 脉冲和连续控制问题的最优方程。整个状态空间不需要连续性或微分假设，也不需要问题参数的稳定性假设。结果表明，如果后干预算子满足沿轨迹属性的某些局部 Lipschitz 连续性，那么脉冲和连续控制问题的值函数也将满足。
In this paper we consider the problem of impulse and continuous control on the jump rate and post jump location parameters of piecewise-deterministic Markov processes (PDP's). In a companion paper we studied the optimal stopping with continuous control problem of PDP's assuming only absolutely continuity along trajectories hypothesis on the final cost function. In this paper we apply these results to obtain optimality equations for the impulse and continuous control problem of PDP's in terms of a set of quasi-variational inequalities as well as on the first jump time operator of the process. No continuity or differential assumptions on the whole state space, neither stability assumptions on the parameters of the problem are required. It is shown that if the post intervention operator satisfies some locally lipschitz continuity along trajectories properties then so will the value function of the impulse and continuous control problem.