| 攀登伪蒙特卡罗积分法在Sobolev和Korobov空间中的随机化误差 |
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| 引用本文： | 岳荣先.攀登伪蒙特卡罗积分法在Sobolev和Korobov空间中的随机化误差[J].应用概率统计,2003,19(3):237-244. |
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| 作者姓名： | 岳荣先 |
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| 作者单位： | 上海师范大学应用数学系,上海,200234 |
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| 基金项目： | This work was supported by a Shanghai NSF grant 00JC14057, a Shanghai Higher Education STF grant 01D01-1 and a NSFC grant 10271078 |
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| 摘 要： | 攀登伪蒙特卡罗积分法是由伪蒙特卡罗与蒙特卡罗方法混合而成的一种新方法，它体现了两者的优点．本文研究这种积分法在Sobolev空间和Korobov空间中的随机化误差．我们证明攀登(λ，t，m，s)-网积分法在这两个空间中的随机化误差的渐近阶为n^3/2logn]^(s-1)/2。
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| 关 键 词： | 随机化伪蒙特卡罗积分法 （t，m，s）－网 |
Randomized Error of Scrambled Net Quadrature for Tensor Product Sobolev and Korobov Spaces |
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| YUE RONGXIAN.Randomized Error of Scrambled Net Quadrature for Tensor Product Sobolev and Korobov Spaces[J].Chinese Journal of Applied Probability and Statisties,2003,19(3):237-244. |
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| Authors: | YUE RONGXIAN |
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| Abstract: | Scrambled quasi-Monte Carlo quadrature is a hybrid of Monte carlo and quasi-Monte Carlo methods, which combines the best of these two methods for integration. This article studies the performance of the scrambled quadrature rules in randomized settings for the tensor product Sobolev and Korobov spaces of integrands. It is shown that the randomized error of the scrambled (A, t, m, s)-nets is of order n-3/2log n](s-1)/2 for these two spaces. |
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| Keywords: | Randomized quasi-Monte Carlo quadrature (t m s)-nets |
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