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

作　　者：吴庆标[1] 

机构地区：[1]浙江大学数学系,浙江杭州310028

出　　处：《浙江大学学报（理学版）》2001年第1期1-6,共6页Journal of Zhejiang University（Science Edition）

基　　金：浙江省自然科学基金资助项目! (10 0 0 0 2 );浙江省教委科研基金资助项目! (G2 980 2 )

摘　　要：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.

关 键 词：MONTE CARLO法 高维积分 随机变量 无偏估计 复连通曲面体 收敛性 重心 

分 类 号：O242.2[理学—计算数学] O241.83[理学—数学]