Strong Mixing Conditions for Random Sequences

随机序列的强混合条件

基本信息

  • 批准号:
    9703712
  • 负责人:
  • 金额:
    $ 6万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    1997
  • 资助国家:
    美国
  • 起止时间:
    1997-07-15 至 2000-06-30
  • 项目状态:
    已结题

项目摘要

9703712 Bradley Strong mixing conditions for random sequences and random fields have been useful in modeling phenomena in the real world in which observations that are ``far apart'' in time or location have only slight influence on each other. In this research, several questions are studied in connection with strongly mixing random sequences, and connections with random fields are discussed briefly. Question 1 deals with a possible ``trichotomy'' for the asymptotic behavior of the partial sums from a strictly stationary, strongly mixing sequence of random variables taking their values in a Banach space. Question 2 deals with the exact location of a part of the ``borderline'' of the central limit theorem under the (Rosenblatt) strong mixing condition. Question 3 deals with the spectral density of random sequences under a certain strong mixing condition. Question 4 deals with a possible connection (or lack of one) between two strong mixing conditions; the relevance of this question to an old conjecture of I.A. Ibragimov is discussed. In the real world, there are many phenomena which appear to be ``weakly dependent,'' in the sense that observations that are ``close'' in time or location may have considerable influence on each other, while observations that are ``far apart'' in time or location have only slight influence on each other. For example, the annual unemployment rate for the year 1998 may have considerable influence on the unemployment rates for the years 1999 and 2000, but will presumably have almost no influence on the employment rate in, say, the year 2050. Similarly, the fluctuations in the wind currents at a given location may be highly correlated with the (wind current) fluctuations ten miles away, but perhaps have no discernible correlation with the fluctuations 3000 miles away. For the modeling of such phenomena, much attention has been devoted in probability theory to a broad type of weak dependence known under the name ``stron g mixing conditions.'' An understanding of ``structural'' properties of strong mixing conditions can help in assessing their appropriateness for the modeling of a given real world phenomenon, and ``laws of averages'' connected with such conditions can provide the foundation for the statistical inference for the given phenomenon. This research deals with several questions concerning both ``structural'' properties and ``laws of averages'' in connection with various strong mixing conditions.
9703712布拉德利 随机序列和随机场的强混合条件已经被证明是 在模拟真实的世界中的现象时很有用,在这个世界中,观察结果“相距甚远” 在时间或地点上彼此之间只有轻微的影响。 在这项研究中,几个 研究了强混合随机序列的问题, 与随机场的连接进行了简要讨论。 问题1:一个可能的 “渐近性”的部分和的渐近行为,从严格平稳, 取值于Banach空间的随机变量的强混合序列。 问题2涉及中央界限的“边界线”的一部分的确切位置 Rosenblatt强混合条件下的一个定理。 问题3涉及 强混合条件下随机序列的谱密度。 问题4 处理两个强混合条件之间可能的联系(或缺乏联系); 这个问题与I.A.的一个古老猜想的相关性。吉莫夫讨论。 在真实的世界中,有许多现象似乎是“弱”的 依赖,“在这个意义上,观察是“接近”的时间或位置可能有 相互之间有相当大的影响,而观察结果在时间上或 位置对彼此的影响很小。 例如,每年的失业率 1998年的失业率可能对2000年的失业率有很大影响, 1999年和2000年,但可能对就业几乎没有影响。 比如说,2050年。同样,在给定的风速下, 位置可能与十英里外的(风流)波动高度相关,但 也许与3000英里外的波动没有明显的相关性。 为 由于对这种现象的建模,在概率论中, 广义的弱相关性,称为强混合条件。安 了解强混合条件的“结构”特性有助于评估 它们对于给定的真实的世界现象的建模的适当性,以及 与这些条件相关的“平均数”可以为统计提供基础。 对给定现象的推理。 这项研究涉及几个问题 关于“结构”性质和“平均律”, 强混合条件

项目成果

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Richard Bradley其他文献

Proposition-valued random variables as information
作为信息的命题值随机变量
  • DOI:
  • 发表时间:
    2010
  • 期刊:
  • 影响因子:
    1.5
  • 作者:
    Richard Bradley
  • 通讯作者:
    Richard Bradley
The kinematics of belief and desire
信念和欲望的运动学
  • DOI:
  • 发表时间:
    2007
  • 期刊:
  • 影响因子:
    1.5
  • 作者:
    Richard Bradley
  • 通讯作者:
    Richard Bradley
Decision Theory: A Formal Philosophical Introduction
决策理论:正式的哲学导论
  • DOI:
  • 发表时间:
    2014
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Richard Bradley
  • 通讯作者:
    Richard Bradley
Making Confident Decisions with Model Ensembles
使用模型集成做出自信的决策
  • DOI:
  • 发表时间:
    2020
  • 期刊:
  • 影响因子:
    0
  • 作者:
    J. Roussos;Richard Bradley;Roman Frigg
  • 通讯作者:
    Roman Frigg
A data-parallel many-source shortest-path algorithm to accelerate macroscopic transport network assignment
加速宏观传输网络分配的数据并行多源最短路径算法
  • DOI:
    10.1016/j.trc.2019.05.020
  • 发表时间:
    2019
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Peter Heywood;Steve C. Maddock;Richard Bradley;David Swain;Ian Wright;M. Mawson;Graham P. Fletcher;Roland Guichard;R. Himlin;P. Richmond
  • 通讯作者:
    P. Richmond

Richard Bradley的其他文献

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{{ truncateString('Richard Bradley', 18)}}的其他基金

Collaborative Research: Highly Ordered Nanoscale Patterns Produced by Ion Bombardment of Solid Surfaces: Theory and Experiment
合作研究:离子轰击固体表面产生的高度有序的纳米级图案:理论与实验
  • 批准号:
    2116753
  • 财政年份:
    2022
  • 资助金额:
    $ 6万
  • 项目类别:
    Continuing Grant
Self-Assembled Nanoscale Patterns Produced by Ion Bombardment of Solid Surfaces
通过离子轰击固体表面产生的自组装纳米级图案
  • 批准号:
    1305449
  • 财政年份:
    2013
  • 资助金额:
    $ 6万
  • 项目类别:
    Continuing Grant
Managing Severe Uncertainty
管理严重的不确定性
  • 批准号:
    AH/J006033/1
  • 财政年份:
    2013
  • 资助金额:
    $ 6万
  • 项目类别:
    Research Grant
Decision Theory with a Human Face
人性化的决策理论
  • 批准号:
    AH/I003118/1
  • 财政年份:
    2012
  • 资助金额:
    $ 6万
  • 项目类别:
    Fellowship
Collaborative Research: Precision Array for Probing the Epoch of Reionization (PAPER)
合作研究:用于探测再电离时代的精密阵列(论文)
  • 批准号:
    1125558
  • 财政年份:
    2011
  • 资助金额:
    $ 6万
  • 项目类别:
    Standard Grant
Choice Theory Network
选择理论网络
  • 批准号:
    AH/H001166/1
  • 财政年份:
    2009
  • 资助金额:
    $ 6万
  • 项目类别:
    Research Grant
Collaborative Research: PAPER: Precision Array to Probe the Epoch on Reionization
合作研究:论文:精密阵列探测再电离时代
  • 批准号:
    0804523
  • 财政年份:
    2008
  • 资助金额:
    $ 6万
  • 项目类别:
    Continuing Grant
Bronze Age metalwork hoards in the landscape of lowland Britain: a pilot study
英国低地景观中的青铜时代金属制品宝库:一项试点研究
  • 批准号:
    AH/E008712/1
  • 财政年份:
    2007
  • 资助金额:
    $ 6万
  • 项目类别:
    Research Grant
Collaborative Proposal for PAPER -- Precision Array to Probe the Epoch of Reionization
PAPER合作提案——精密阵列探测再电离时代
  • 批准号:
    0607759
  • 财政年份:
    2006
  • 资助金额:
    $ 6万
  • 项目类别:
    Standard Grant
Mathematical Sciences: Strong Mixing Conditions for Random Sequences and Random Fields
数学科学:随机序列和随机场的强混合条件
  • 批准号:
    9500307
  • 财政年份:
    1995
  • 资助金额:
    $ 6万
  • 项目类别:
    Standard Grant

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Investigation of mixing and diffusion mechanisms with phase-separation of multi-component fluid under cryogenic high-pressure conditions
低温高压条件下多组分流体相分离的混合和扩散机制研究
  • 批准号:
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职业:极端​​条件下冲击加速变密度流的转变、湍流和混合
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CAREER: Transition, Turbulence and Mixing in Shock-Accelerated Variable Density Flows at Extreme Conditions
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