题目：Random star discrepancy based on stratified sampling
报告人： 冼军
报告时间：2024年3月21日 15:00-16:00
地点：综合楼644会议室
报告人简介：
冼军, 男, 博士, 教授, 博士生导师, 国家优秀青年基金获得者，现为中山大学逸仙学者、中国数学会理事、广东省数学会理事、广东省工业与应用数学学会副理事长。2004年毕业于中山大学获理学博士学位, 同年进入浙江大学数学博士后流动站, 2006年博士后出站至今在中山大学数学学院工作。主要研究方向为小波分析与应用调和分析、采样理论及其在信号处理中的应用。在Appl. Comput. Harmon. Anal., Inverse Probl., J. Fourier Anal. Appl., Proc. Amer. Math. Soc., J. Approx. Theory等国内外主流专业期刊发表多篇关于信号的采样与重构的理论及其应用的论文, 很多结果获得同行们的关注。曾作为项目负责人主持多项国家级和省部级基金项目。
报告摘要：
In this talk, we consider the estimation of the expected star discrepancy. First, the expected star discrepancy upper bound is obtained for the jittered sampling. This improves the upper bound derived in B. Doerr(Math. Comp. 2022, 1871-1892). Second, the strong partition principle of the star discrepancy version is obtained, which proves that the expected star discrepancy of stratified sampling is smaller than that of simple random sampling for any equal-measure partition. This partially solves open question 2 in M. Kiderlen and F. Pausinger(J. Complexity, 2022, 101616). In the end, we consider the estimation of the weighted star discrepancy. A better weighted probabilistic star discrepancy bound than the use of plain Monte Carlo point sets is provided in terms of convergence order, i.e., the convergence order of the weighted probabilistic bound is improved from O(N^(-1/2)) to O(N^(1/2-1/(2d))*(lnN)^(1/2)).
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