Strong Mixing Conditions for Random Sequences

随机序列的强混合条件

• 批准号: 9703712
• 负责人: Richard Bradley
• 金额: $ 6万
• 依托单位: Indiana University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 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
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9703712&HistoricalAwards=false
• 关键词: Strong; Mixing; Conditions; Random; Sequences

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 Bradley的强烈混合条件和随机序列的强烈混合条件在现实世界中建模现象很有用，在现实世界中，在时间或位置上``远距离''的观察结果彼此仅具有轻微的影响。 在这项研究中，研究了几个问题，该问题与强烈混合随机序列有关，并简要讨论与随机字段的连接。 问题1介绍了可能的``三分法''可能是从严格固定的，强烈混合随机变量的渐近总和中的渐近行为，将其值在Banach空间中占据。 问题2涉及中央限制定理（Rosenblatt）强混合条件下的``边界线''一部分的确切位置。 问题3涉及在某种强烈混合条件下随机序列的光谱密度。 问题4涉及两个强大的混合条件之间可能的连接（或缺乏）； 这个问题与I.A.的旧猜想的相关性讨论了易卜拉吉莫夫。 在现实世界中，有许多现象似乎是``弱依赖''，从某种意义上说，在时间或位置上````近''''的观察结果可能会彼此产生相当大的影响，而及时或位置的观察结果只有``远距离''的观察结果对彼此只有轻微的影响。 例如，1998年的年度失业率可能会对1999年和2000年的失业率产生重大影响，但大概几乎不会对2050年的就业率没有影响。同样，同样，在特定位置，风流的波动与（风电流）的相关性很大，但与（风电流）相距不相同，可能与（相距十英里）相关。 对于这种现象的建模，在概率理论中已经将很多关注投入到以``'stron g混合条件''的名称所知的广泛类型的弱依赖性。对````stron g''混合条件''的了解。 现象。 这项研究涉及有关``结构''属性和``平均定律''的几个问题。