Optimal error bound of restricted Monte Carlo integration on anisotropic Sobolev classes  

作　　者：GAO Wenhua YE Peixin WANG Hui 

机构地区：[1]College of Mathematics and System Sciences, Xinjiang University, Urumqi 8301146, China [2]School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071,China [3]Department of Mathematics, Ily Teachers＇ College, Yining 835000, China [4]College of Science, Hehai University, Nanjing 210098, China

出　　处：《Progress in Natural Science:Materials International》2006年第6期588-593,共6页自然科学进展·国际材料（英文版）

基　　金：Supported by National Natural Science Foundation of China (Grant Nos. 10261007 and 10501026)Tianyuan Fund for Mathematics (Grant No.10426020) and the fund of Nankai University

摘　　要：We study the restricted Monte Carlo integration error for anisotropie Sobolev classes. Results prove that with O（log2 n ） random bits we have the optimal order for the n-th minimal Monte Carlo integration error with arbitrary random numbers.我们为各向异性的 Sobolev 班学习限制蒙特卡罗集成错误。结果与 O (木头 <SUB>2</SUB> n ) 证明那我们有的随机的位为有任意的随机的第 n 个最小的蒙特卡罗集成错误的最佳的顺序数。

关 键 词：Monte Carlo integration random bits anisotropic Sobolev classes. 

分 类 号：O242[理学—计算数学]