复连通曲面体高维积分的Monte Carlo法

On the calculation of higher dimensional integration with a complex connected curved polyhedron domain by Monte Carlo methods

本文讨论了用 Monte Carlo法求积分区域为复连通曲面体的高维积分 ,即用 Monte Carlo法估计下面形式的高维积分 :I =∫G-∪sj=1Gj…∫f (x1,x2 ,… ,xn) dx1dx2 … dxn,其中 n为积分维数 ,Gj G(j=1,2 ,… ,s) ,分别根据 G体积已知 ,Gj(j =1,2 ,… ,s)体积未知和 G,Gj(j=1,2 ,… ,s)体积都未知情形得出估计法、收敛性定理和具体算法 ,另外 ,也对求复连通曲面体的重心问题进行分析 ,得出估计法和收敛性定理 .

The Monte Carlo integration that the domain of integration is complex connected curved polyhedron was discussed in this paper. \$I=∫\-\{G-∪sj=1G\-j\}\:∫f(x\-1,x\-2,\:,x\-n)\%d\%x\-1\%d\%x\-2\:\%d\%x\-n\$, where \%n\% is the dimension, \$G\-jG(j=1,2,\:,s)\$. In known and unknown volume of the integral domain , two estimation methods and convergence theorems were presented. Estimating barycenter of complex connected curved polyhedron was also discussed.