论文标题
与线性噪声的随机热方程式线性季度控制问题的时空离散性的强误差估计值
Strong Error Estimates for a Space-Time Discretization of the Linear-Quadratic Control Problem with the Stochastic Heat Equation with Linear Noise
论文作者
论文摘要
我们提出了一个时间瞬间，基于有限元素的时空离散化，该时空的最佳条件是由随机热量方程式的随机线性季度最佳控制问题，由随机热方程式由$ [x（t）+σ（t）+σ（t）] dw（t）的线性噪声驱动的随机热方程，dw（t）] dw（t）$，以及prove-prove最佳crevengence crevengence w.r.r.t.t。空间和时间离散参数。特别是，我们采用随机riccati方程作为适当的分析工具来处理线性噪声，从而扩展了早期工作的适用性[16]，其中误差分析仅限于附加噪声。
We propose a time-implicit, finite-element based space-time discretization of the necessary and sufficient optimality conditions for the stochastic linear-quadratic optimal control problem with the stochastic heat equation driven by linear noise of type $[X(t)+σ(t)]dW(t)$, and prove optimal convergence w.r.t. both, space and time discretization parameters. In particular, we employ the stochastic Riccati equation as a proper analytical tool to handle the linear noise, and thus extend the applicability of the earlier work [16], where the error analysis was restricted to additive noise.
