论文标题
零和线性季度随机差异游戏的奇异扰动
Singular Perturbation of Zero-Sum Linear-Quadratic Stochastic Differential Games
论文作者
论文摘要
我们在有限的时间范围内研究了一类零和线性二次随机差异游戏，该游戏由多尺度状态方程管理。可以利用该问题的多规定性质，以将相关的广义riccati方程重新制定为确定性的奇异扰动问题。在这样做时，我们表明，对于足够小的$ε$，存在对相关的广义riccati方程的解决方案，可以通过对脱钩的一对差分和代数riccati方程的解决方案来保证，并且具有降低的维度。此外，我们能够通过构建近似反馈策略并观察限制值函数来制定对游戏问题的价值函数的一对渐近估计。
We investigate a class of zero-sum linear-quadratic stochastic differential games on a finite time horizon governed by multiscale state equations. The multiscale nature of the problem can be leveraged to reformulate the associated generalised Riccati equation as a deterministic singular perturbation problem. In doing so, we show that, for small enough $ε$, the existence of solution to the associated generalised Riccati equation is guaranteed by the existence of a solution to a decoupled pair of differential and algebraic Riccati equations with a reduced order of dimensionality. Furthermore, we are able to formulate a pair of asymptotic estimates to the value function of the game problem by constructing an approximate feedback strategy and observing the limiting value function.
