Infinite-Dimensional Quadrature and Approximation of Distributions
Infinite-Dimensional Quadrature and Approximation of Distributions
复制标题
无限维求积和分布逼近
DOI：
10.1007/s10208-008-9029-x
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发表时间：
2009
影响因子：
3
通讯作者：
K. Ritter
中科院分区：
文献类型：
--
作者：
J. Creutzig;S. Dereich;T. Müller;K. Ritter
我们通过确定性和随机（Monte Carlo）算法研究Lipschitz功能在Banach空间上的数值整合。该二次问题显示与量化问题以及基本概率度量的平均kolmogorov宽度密切相关。除了一般环境外，我们特别分析了扩散过程的高斯测量和分布。我们以其成本来得出每种算法的最坏情况误差的下限，并且我们提出了匹配的上限，达到对数以及相应的几乎最佳算法。作为辅助结果，我们确定用于扩散过程的量化数字和kolmogorov宽度的渐近行为。
We study numerical integration of Lipschitz functionals on a Banach space by means of deterministic and randomized (Monte Carlo) algorithms. This quadrature problem is shown to be closely related to the problem of quantization and to the average Kolmogorov widths of the underlying probability measure. In addition to the general setting, we analyze, in particular, integration with respect to Gaussian measures and distributions of diffusion processes. We derive lower bounds for the worst case error of every algorithm in terms of its cost, and we present matching upper bounds, up to logarithms, and corresponding almost optimal algorithms. As auxiliary results, we determine the asymptotic behavior of quantization numbers and Kolmogorov widths for diffusion processes.
影响因子：
2.7
作者：
Giles, Michael B.
通讯作者：
Giles, Michael B.