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
• 负责人: Richard Bradley
• 金额: $ 4万
• 依托单位: Indiana University
• 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: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500307&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Strong; Mixing; Conditions

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 Bradley 摘要 该提案涉及满足强混合条件的随机序列和随机场的研究。 如果（根据适当的标准）“过去”和“未来”之间的随机“依赖性”量随着“过去”和“未来”之间的“时间”量而变得一致任意小，则称随机序列满足“强混合条件”过去和未来变得足够大。 对于随机场，“强混合”的概念是相似的，涉及随着观察组之间的“距离”变大，它们之间的一致渐近独立性。 对于这样的随机序列和随机场，“结构性质”和极限定理都被研究。 特别是，该提案涉及主要研究者最近的一些工作的延续，其中在强混合假设下对某一类随机场证明的中心极限定理比其他研究人员早期的类似定理要弱得多。 该提案涉及涉及“弱依赖”的概率模型的研究，其中“过去”和“现在”可能对“不久的将来”产生相当大的影响，但对“遥远的未来”的影响要小得多。例如，全国年平均失业率是符合这一模型的众多现象之一； 1995 年的失业率可能会对 1996 年或 1997 年的失业率产生相当大的影响，但对 2050 年的失业率影响不大。该提案涉及对弱依赖性，以及此类模型可能满足的各种长期“平均定律”。 特别是，该提案的一部分涉及主要研究者最近的一些工作的延续，这些工作大大扩展了已知满足某些重要平均定律的弱依赖模型的类别。该提案还涉及类似类型的概率模型的研究，其中观察结果按位置而不是时间分隔。