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
基本信息
- 批准号:9500307
- 负责人:
- 金额:$ 4万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:1995
- 资助国家:美国
- 起止时间:1995-06-01 至 1997-05-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
9500307 Bradley Abstract This proposal concerns the study of random sequences and random fields satisfying strong mixing conditions. A random sequence is said to satisfy a "strong mixing condition" if (according to an appropriate criterion) the amount of stochastic "dependence" between the "past" and the "future" becomes uniformly arbitrarily small as the amount of "time" between past and future becomes sufficiently large. For random fields, the notions of "strong mixing" are similar, involving the uniform asymptotic independence between sets of observations as the "distance" between them becomes large. For such random sequences and random fields, both "structural properties" and limit theorems are investigated. In particular, this proposal involves a continuation of some recent work by the principal investigator in which the central limit theorem is proved for a certain class of random fields under strong mixing assumptions considerably weaker than in earlier similar theorems by other researchers. This proposal concerns the study of probabilistic models that involve "weak dependence," in which the "past" and "present" might have considerable influence on the "near future" but much less influence on the "far future." For example, the average annual national unemployment rate is one of many phenomena which appear to fit such a model; the unemployment rate for the year 1995 could presumably have considerable effect on the rate for the year 1996 or 1997 but not much effect on the rate for the year 2050. This proposal involves an investigation into various kinds of "structural properties" of probabilistic models of weak dependence, and also various long-term "laws of averages" that such models might satisfy. In particular, part of this proposal involves a continuation of some recent work by the principal investigator which considerably enlarges the class of weak dependence models that are known to satisfy a certain important law of averages. This proposal also concerns the study of similar types of probabilistic models in which observations are separated by location instead of time.
9500307布拉德利摘要这一建议涉及研究满足强混合条件的随机序列和随机场。一个随机序列被称为满足“强混合条件”,如果(根据适当的标准)“过去”和“未来”之间的随机“依赖”量变得一致地任意小,而过去和未来之间的“时间”量变得足够大。对于随机场,“强混合”的概念是相似的,包括随着观测集合之间的“距离”变大,它们之间的一致渐近独立性。对于这种随机序列和随机场,我们研究了它们的“结构性质”和极限定理。特别地,这一建议涉及到主要研究者最近的一些工作的继续,在强混合假设下证明了某类随机场的中心极限定理,比其他研究者以前的类似定理要弱得多。这一建议涉及涉及“弱依赖”的概率模型的研究,在该模型中,“过去”和“现在”可能对“近未来”有相当大的影响,但对“远未来”的影响要小得多。例如,全国年平均失业率是似乎符合这种模型的许多现象之一;1995年的失业率可能对1996年或1997年的失业率有相当大的影响,但对2050年的失业率影响不大。这一建议涉及对弱相依性概率模型的各种“结构性质”的调查,以及这些模型可能满足的各种长期“平均定律”。特别是,这一建议的一部分涉及首席研究员最近的一些工作的继续,这项工作大大扩大了已知满足某一重要平均定律的弱相关性模型的类别。这一建议还涉及对类似类型的概率模型的研究,在这种模型中,观测按位置而不是按时间分开。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Richard Bradley其他文献
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
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
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
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2116753 - 财政年份:2022
- 资助金额:
$ 4万 - 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
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1305449 - 财政年份:2013
- 资助金额:
$ 4万 - 项目类别:
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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:
$ 4万 - 项目类别:
Standard 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
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0804523 - 财政年份:2008
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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
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AH/E008712/1 - 财政年份:2007
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PAPER合作提案——精密阵列探测再电离时代
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0607759 - 财政年份:2006
- 资助金额:
$ 4万 - 项目类别:
Standard Grant
Strong Mixing Conditions for Random Sequences
随机序列的强混合条件
- 批准号:
9703712 - 财政年份:1997
- 资助金额:
$ 4万 - 项目类别:
Standard Grant
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