In this article, a notion of viscosity solutions is introduced for second-order Hamilton–Jacobi–Bellman (HJB) equations with delays associated with optimal control problems for stochastic differential equations with delays. We identify the value functional of optimal control problem as the unique viscosity solution to the second-order HJB equation.

中文翻译：

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具有时滞的二阶 Hamilton–Jacobi–Bellman 方程的粘度解的概念

在本文中，为具有时滞的二阶 Hamilton-Jacobi-Bellman (HJB) 方程引入了粘度解的概念，该方程与具有时滞的随机微分方程的最优控制问题相关。我们将最优控制问题的值泛函确定为二阶 HJB 方程的唯一粘度解。