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，这些随机过程表现出长程相关性和非线性等特征，并在这一令人兴奋的新领域教育统计学家和其他科学家。与独立性假设下的成熟理论相比，为具有这些特征的过程建立极限理论具有相当大的挑战性。主要研究者提出了一种强有力的基于鞅的方法，并研究了这类过程的谱估计、经验过程、非参数估计和其他相关的渐近问题，具有长程相关性和非线性的过程存在于各个领域，包括计算机网络、通信、金融、地质、水文、计量经济学和大气科学等。该提案中开发的研究成果的应用将有助于测试和证明科学家在这些领域提出的主张。特别是，PI开发了识别温度和臭氧序列趋势的方法学，并为气象学家对气候变化模式的主张提供了统计推理。