Recurrence and Transience of Optimal Feedback Processes Associated with Bellman Equations of Ergodic Type
Recurrence and Transience of Optimal Feedback Processes Associated with Bellman Equations of Ergodic Type
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DOI：
10.1137/090772678
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发表时间：
2011-09
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影响因子：
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通讯作者：
Naoyuki Ichihara
中科院分区：
文献类型：
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作者：
Naoyuki Ichihara
本文讨论了线性(指数)二次高斯控制中典型的遍历型Bellman方程。我们感兴趣的是根据Bellman方程解的定性性质给出相关的最优反馈扩散的递归-瞬变准则。为了建立这样的准则，我们提出了一种基于Lyapunov方法的新方法。事实证明，方程的某种凸性在我们的论证中起着关键作用。
The paper is concerned with ergodic-type Bellman equations arising typically in linear (exponential) quadratic Gaussian control. We are interested in giving recurrence-transience criteria for associated optimal feedback diffusions in terms of qualitative properties of solutions to the Bellman equation. To establish such criteria, we propose a new approach which is based on the Lyapunov method. It turns out that a certain convexity of the equation plays a key role in our arguments.