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

We study the restricted Monte Carlo integration error for anisotropic 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.

作 者： GAO Wenhua YE Peixin WANG Hui   作者單位： GAO Wenhua(College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China)

YE Peixin(School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China)

WANG Hui(Department of Mathematics, Ily Teachers' College, Yining 835000, China;College of Science, Hehai University, Nanjing 210098, China) 

刊 名： 自然科學進展（英文版）  SCI 英文刊名： PROGRESS IN NATURAL SCIENCE  年，卷(期)： 2006 16(6)  分類號： N1  關(guān)鍵詞： Monte Carlo integration   random bits   anisotropic Sobolev classes  

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