Information complexity of Monte Carlo integration in multivariate functions with mixed smothness

摘要：

In this paper, we investigate information complexity of integration of the Sobolev classes with bounded mixed derivative in the Monte Carlo setting. We develop Monte Carlo algorithms for integration of functions from these classes and analyze their convergence rates. Comparing our result with the known convergence rates in the deterministic setting, we see that Monte Carlo algorithms bring a essential speed-up.

关键词： integration problem Monte Carlo algorithm Sobolev space with mixed derivative information complexity

作者: Duan liqin Ye peixin

作者单位: Institute of Mathematics, Hangzhou Dianzi University, Hangzhou 310018, China School of Mathematics, Nankai University, Tianjin 300071, China

会议类型: 国际会议

会议名称: 4th International Conference on Measuring Technology and Mechatronics Automation(第四届检测技术与机电自动化国际会议 ICMTMA 2012)

会议地点: 三亚

会议语种:英文

页码: 1321-1324

在线出版日期: 2012-01-06（万方平台首次上网日期，不代表论文的发表时间）