论文标题
线性季节随机Volterra控制I：因果反馈策略
Linear-quadratic stochastic Volterra controls I: Causal feedback strategies
论文作者
论文摘要
在本文中，我们制定并研究了具有单数和非卷积型系数的随机Volterra积分方程（SVIE）在线性季节控制问题（SVIE）中产生的因果反馈策略的概念。我们表明，存在一个独特的解决方案，我们称之为因果反馈策略相关的受控SVIE的闭环系统。此外，我们引入了两个名为II类型的新型方程式扩展后向后的伏尔泰拉积分方程和lyapunov-volterra方程式，我们证明了在因果反馈策略框架中受控SVIE的二次功能的双重性原理和代表性公式。
In this paper, we formulate and investigate the notion of causal feedback strategies arising in linear-quadratic control problems for stochastic Volterra integral equations (SVIEs) with singular and non-convolution-type coefficients. We show that there exists a unique solution, which we call the causal feedback solution, to the closed-loop system of a controlled SVIE associated with a causal feedback strategy. Furthermore, introducing two novel equations named a Type-II extended backward stochastic Volterra integral equation and a Lyapunov--Volterra equation, we prove a duality principle and a representation formula for a quadratic functional of controlled SVIEs in the framework of causal feedback strategies.
