论文标题
希尔伯特空间中二阶路径依赖汉密尔顿 - 雅各比 - 贝尔曼方程的粘度解决方案
Viscosity Solutions to Second Order Path-Dependent Hamilton-Jacobi-Bellman Equations in Hilbert Spaces
论文作者
论文摘要
在本文中，引入了与二阶路径依赖性汉密尔顿 - 雅各比 - 贝尔曼（PHJB）方程相关的粘度解决方案的概念，该方程与Hilbert Space中路径依赖性随机演化方程相关的最佳控制问题相关。我们将最佳控制问题的价值功能视为相关PHJB方程的唯一粘度解决方案。我们还表明，我们的粘度解决方案概念与经典解决方案的相应概念一致，并满足稳定性。
In this article, a notion of viscosity solutions is introduced for second order path-dependent Hamilton-Jacobi-Bellman (PHJB) equations associated with optimal control problems for path-dependent stochastic evolution equations in Hilbert spaces. We identify the value functional of optimal control problems as unique viscosity solution to the associated PHJB equations. We also show that our notion of viscosity solutions is consistent with the corresponding notion of classical solutions, and satisfies a stability property.
