CAREER: Asymptotics of random processes and their applications

职业：随机过程的渐近及其应用

• 批准号: 0448704
• 负责人: Wei Biao Wu
• 金额: --
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-03-01 至 2011-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0448704&HistoricalAwards=false
• 关键词: CAREER; Asymptotics; random; processes; their

The proposal aims to advance statistical theory for randomprocesses that exhibit features like long-range dependence andnonlinearities, and to educate both statisticians and othersscientists in this new exciting area. Compared to thewell-developed theory under the independence assumption, it isconsiderably more challenging to establish a limit theory forprocesses with such features. The Principal Investigator proposesa powerful martingale based method and studies spectralestimation, empirical processes, nonparametric estimation andother related asymptotic problems for such processes.Processes with long-range dependence and nonlinearities occur invarious fields, including computer networks, communication,finance, geology, hydrology, econometrics and atmospheric scienceamong others. Applications of the research results developed inthe proposal would help test and justify claims made by scientistsin such fields. In particular, the PI develops statisticalmethodology to identify trends in temperature and ozone sequencesand provides statistical reasoning for meteorologists' claims onclimate change patterns.

该提案旨在推进随机过程的统计理论，这些过程表现出长期相关性和非线性等特征，并在这个新的令人兴奋的领域对统计学家和其他科学家进行教育。与独立假设下的成熟理论相比，建立具有这种特征的过程的极限理论具有相当大的挑战性。主要研究人员提出了一种强大的基于鞅的方法，研究了这类过程的谱估计、经验过程、非参数估计等相关的渐近问题，涉及计算机网络、通信、金融、地质学、水文学、计量经济学和大气科学等多个领域。该提案中开发的研究成果的应用将有助于检验和证明科学家在这些领域的说法是正确的。特别是，PI开发了统计方法来确定温度和臭氧序列的趋势，并为气象学家关于气候变化模式的主张提供统计推理。