Probability and Statistics Seminar——Periodic measures and Wasserstein distance for analysing periodicity of time series datasets
报告人：Huaizhong Zhao (Durham)
时间：2023-04-10 14:00-15:00
地点：Room 1114, Sciences Building No. 1
Abstract: In this talk, I will talk about the results in a new paper, jointly written with Chunrong Feng and Yujia Liu, mainly on the probability foundation of the periodic measure approach inanalysing periodicity of a dataset. It is based on recent work of random periodic processes. While random periodic paths provide a pathwise model for time series datasets with a periodic pattern, their law is a periodic measure and gives a statistical description and the ergodic theory offers a scope of statistical analysis. The connection of a sample path and the periodic measure is revealed in the law of large numbers (LLN). We prove first the period is actually a deterministic number and then for discrete processes, {B\'{e}zout's identity comes in naturally in the LLN along an arithmetic sequence of an arbitrary increment.} The limit is a periodic measure whose period is equal to the greatest common divisor between the test period and the true period of the random periodic process. This leads to a new scheme of detecting random periodicity of a dataset and finding its period, as an alternative to the Discrete Fourier Transformation (DFT) and periodogram approach. We find that in some situations, the classical method does not work robustly, but the new one can work efficiently. We prove that the periodicity is quantified by the Wasserstein distance, in which the convergence of empirical distributions is established.
Bio: 赵怀忠在1984年毕业于山东大学数学系数学专业，1990年在中国科学院应用数学所获得博士学位（动力系统)，1995年取得英国华威大学数学研究所博士学位（随机分析）。先后在中科院应用数学研究所、英国华威大学数学研究所、意大利国际理论物理中心（ICTP）、英国斯旺西大学、美国加利福尼亚大学尔湾分校、英国拉夫堡大学任职，现为英国杜伦大学教授，山东大学高层次人才特聘教授。曾入选英国自然科学基金委资深人才（EPSRC Established Career Fellowship)、上海市海外高层次人才、国家海外高层次人才。先后在Mem. AMS、CMP、JFA、JDE、SICON、SINUM、SIMA，CNSNS等期刊上发表论文70余篇。主要研究方向为随机分析，涉及随机微分方程/随机偏微分方程、非线性期望，特别是随机动力学、遍历性理论等。
