论文标题
基于数字网和序列的立方体上的加权集成
Weighted integration over a cube based on digital nets and sequences
论文作者
论文摘要
准蒙特卡洛（QMC）方法是相等的重量正交规则，可相对于均匀度量，近似于单位立方体的积分。在本文中，我们讨论了与任意立方体定义的一般产品度量的QMC集成。我们只要求累积分布函数可逆。我们开发出一个最坏的案例误差，并研究了误差对点数和数字网和序列的尺寸以及多项式晶格点集的依赖性，这些晶格点集使用逆累积分布函数映射到域。我们不需要概率密度函数的任何平滑度属性，最坏情况误差不取决于密度函数的特定选择及其平滑度。多项式晶格规则的组成部分构建基于仅取决于立方体大小但与产品度量无关的标准。
Quasi-Monte Carlo (QMC) methods are equal weight quadrature rules to approximate integrals over the unit cube with respect to the uniform measure. In this paper we discuss QMC integration with respect to general product measures defined on an arbitrary cube. We only require that the cumulative distribution function is invertible. We develop a worst-case error bound and study the dependence of the error on the number of points and the dimension for digital nets and sequences as well as polynomial lattice point sets, which are mapped to the domain using the inverse cumulative distribution function. We do not require any smoothness properties of the probability density function and the worst-case error does not depend on the particular choice of density function and its smoothness. The component-by-component construction of polynomial lattice rules is based on a criterion which depends only on the size of the cube but is otherwise independent of the product measure.
