论文标题
具有随机路径依赖的系数和随机路径依赖的汉密尔顿 - 雅各比方程的受控普通微分方程
Controlled Ordinary Differential Equations with Random Path-Dependent Coefficients and Stochastic Path-Dependent Hamilton-Jacobi Equations
论文作者
论文摘要
本文致力于普通微分方程的随机最佳控制问题，允许路径依赖性和可测量的随机性。与确定性路径依赖性情况相反，事实证明，值函数是路径空间上的一个随机场，其特征是随机路径依赖性汉密尔顿 - 雅各布（SPHJ）方程。提出了粘度解决方案的概念，并证明该值函数是相关SPHJ方程的唯一粘度解决方案。
This paper is devoted to the stochastic optimal control problem of ordinary differential equations allowing for both path-dependence and measurable randomness. As opposed to the deterministic path-dependent cases, the value function turns out to be a random field on the path spaces and it is characterized by a stochastic path-dependent Hamilton-Jacobi (SPHJ) equation. A notion of viscosity solution is proposed and the value function is proved to be the unique viscosity solution to the associated SPHJ equation.
