Estimation from Dynamical Systems and Individual Sequences

动力系统和个体序列的估计

• 批准号: 9971964
• 负责人: Andrew Nobel
• 金额: $ 7.5万
• 依托单位: University of North Carolina at Chapel Hill
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-09-01 至 2003-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9971964&HistoricalAwards=false
• 关键词: Estimation; Dynamical; Systems; Individual; Sequences

DMS 9971964 Estimation from Dynamical Systems and Individual SequencesAndrew B. Nobel, University of North Carolina, Chapel HillABSTRACT:The advent of modern computing and the recent interest in chaos have focussed increasing attention on deterministic systems that exhibit random behavior. Statistical analysis of such systems is often complicated by the fact that measurements of their behavior can exhibit very long-range dependence. The Principal Investigator is studying non-parametric estimation from ergodic processes and individual sequences, with particular emphasis on processes and sequences that arise from measurement of a dynamical system. He is developing and proving the consistency of schemes for the following problems: (i) estimating the map generating a given discrete time dynamical system; (ii) estimating the stationary density and Lyapunov exponents of a dynamical system; and (iii) density and regression estimation from individual sequences. In addition, the P.I. is seeking to characterize deterministic sequences and to estimate their induced transformations.The advent of modern computing and recent scientific interest in chaos have focussed increasing attention on physical systems that are governed by deterministic laws, but exhibit erratic or unpredictable behavior that is characteristic of random phenomena. Dynamical systems of this sort have found application in such diverse areas as medical diagnostics and weather prediction.The Principal Investigator (P.I.) is developing statistical methods that can be used estimate the underlying properties of a dynamical system from observations of the system as it evolves in time. This is important if one wishes to predict or control the future behavior of the system. The P.I. is developing methods to estimate the rule that dictates the evolution of the system over a single unit of time. He is also developing methods to assess the sensitivity of the system to its initial conditions: if the system is started off in two very similar states, how different will it look later? The P.I. is seeking methods that will be effective for a wide variety of systems, including those whose measurements exhibit dependence over very long time scales.

DMS 9971964从动态系统和单个序列的估计北卡罗来纳大学，北卡罗来纳大学，教堂hillabstract：现代计算的出现以及对混乱的最新兴趣的兴趣越来越多地关注表现随机行为的确定性系统。 这种系统的统计分析通常会使其行为的测量表现出非常长的依赖性，这通常使其复杂化。 首席研究者正在研究从沿着厄运过程和单个序列的非参数估计，特别强调了由动态系统测量的过程和序列。 他正在开发并证明方案在以下问题上的一致性：（i）估算产生给定离散时间动态系统的地图； （ii）估计动力系统的固定密度和lyapunov指数； （iii）来自各个序列的密度和回归估计。 此外，P.I.试图表征确定性序列并估算其诱导的转变。现代计算的出现和最近对混乱的科学兴趣的出现将越来越多的关注越来越多地关注受确定性定律管辖的物理系统，但表现出不稳定或不可预测的行为，这是随机现象的特征。 这种动态系统发现在医学诊断和天气预测等不同领域的应用。主要研究者（P.I.）正在开发可使用的统计方法，可以估计动态系统的潜在特性，从系统的观察中随着时间的推移而演变。 如果要预测或控制系统的未来行为，这一点很重要。 P.I.正在开发方法来估计在单个时间单位中决定系统演变的规则。 他还在开发评估系统对其初始条件的敏感性的方法：如果系统以两个非常相似的状态启动，以后会有何不同？ P.I.正在寻求对各种系统有效的方法，包括那些测量结果在很长的尺度上表现出依赖性的方法。