论文标题
蒙特卡洛在维纳空间上的立方体建设
Monte Carlo construction of cubature on Wiener space
论文作者
论文摘要
在本文中，我们研究了数学优化在Wiener空间上的构造中的数学优化的应用，这是Lyons和Victoir引入的随机微分方程的弱近似方法（Wiener Space上的Cubature，Proc。R.Soc。Lond。A460，169---198）。在对Wiener空间的立方体理论进行了简要回顾之后，我们表明可以通过蒙特卡洛采样和线性编程获得一般维度和程度的立方体公式。本文还包括随机Tchakaloff定理的扩展，从技术上讲，该定理可以证明我们的主要结果。
In this paper, we investigate application of mathematical optimization to construction of a cubature formula on Wiener space, which is a weak approximation method of stochastic differential equations introduced by Lyons and Victoir (Cubature on Wiener Space, Proc. R. Soc. Lond. A 460, 169--198). After giving a brief review of the cubature theory on Wiener space, we show that a cubature formula of general dimension and degree can be obtained through a Monte Carlo sampling and linear programming. This paper also includes an extension of stochastic Tchakaloff's theorem, which technically yields the proof of our primary result.
