论文标题
一阶路径依赖性HJB方程的粘度解决方案
Viscosity Solutions to First Order Path-Dependent HJB Equations
论文作者
论文摘要
在本文中，针对一阶路径依赖性汉密尔顿 - 雅各比 - 贝尔曼（HJB）方程引入了粘度解决方案的概念。我们将最佳控制问题的价值功能视为相关HJB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 first order path-dependent Hamilton-Jacobi-Bellman (HJB) equations associated with optimal control problems for path-dependent differential equations. We identify the value functional of the optimal control problems as a unique viscosity solution to the associated HJB equations. We also show that our notion of viscosity solutions is consistent with the corresponding notion of classical solutions, and satisfies a stability property.
