论文标题
由征费噪声驱动的随机汉堡方程的动态编程
Dynamic Programming of Stochastic Burgers Equation Driven by Levy Noise
论文作者
论文摘要
在这项工作中，我们研究了由高斯和征税类型噪声扰动的随机汉堡方程的最佳控制，其分布式控制过程作用于状态方程。我们使用二阶的动态编程方法汉密尔顿 - 雅各布 - 贝尔曼（HJB）方程，该方程由与随机控制问题相关的征费度量的全差异算子组成。使用与随机汉堡方程和紧凑性参数相对应的过渡半群的正规化特性，我们解决了HJB方程和结果反馈控制问题。
In this work, we study the optimal control of stochastic Burgers equation perturbed by Gaussian and Levy type noises with distributed control process acting on the state equation. We use the dynamic programming approach for the second order Hamilton-Jacobi- Bellman (HJB) equation consisting of an integro-differential operator with Levy measure associated with the stochastic control problem. Using the regularizing properties of the transition semigroup corresponding to the stochastic Burgers equation and compactness arguments, we solve the HJB equation and the resultant feedback control problem.
