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Uniform asymptotic independence on essential parts of a sequence of random indices and sufficient conditions of limit theorems with random indices

随机指标序列基本部分的一致渐近独立性以及随机指标极限定理的充分条件

基本信息

批准号：
10640144
负责人：
SUGIMAN Ikuo
金额：
$ 0.32万
依托单位：
FUKUOKA UVNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 1999
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640144/
关键词：
Limit theorem Stopping rule Asymptotic independence Stochastic Processes 確率添字 Anacomba 条件

项目摘要

In this research, we studied a generalization of sufficient conditions for (random) limit theorems of {XィイD2τnィエD2} , Where {XィイD2nィエD2} was a lattice of random elements of a metric space and {τィイD2nィエD2} was a lattice of random multidimensional indices.We defined the Essential ε-independence condition of {XィイD2nィエD2} for {τィイD2nィエD2} as a generalized version of the uniform and asymptotic independence condition and gave the random limit theorem on this condition in this research. These condition and result are generalizations for the Uniform ε-independence condition and the random limit theorem on that condition. Moreover, we showed these were not only so, but also generalizations for the probabilistic uniform continuity (Anscombe) condition which was widely applicable and was another condition did not look like independence conditions at all. And we defined another version of the Essential ε-independence condition and we showed that this was equivalent that it held the random limit theorems for all lattice of random indices of some class, if the metric space {XィイD2nィエD2} took values on was separable.After this, we shall study for the methods of constitution of useful stopping rules in the set of random indices extended in this research.

本文研究了{X D2τn D2}的（随机）极限定理的充分条件的推广，其中{X D2n D2}是度量空间中随机元素的格，{τ D2n D2}是随机多维指标的格。本文定义了{τ τ￣￣D2n￣￣D2}对于{X￣￣D2n￣￣D2}的基本ε-独立条件，作为一致渐近独立条件的推广形式，并给出了该条件的随机极限定理。这些条件和结果是对一致ε无关条件和该条件下的随机极限定理的推广。此外，我们证明了这些不仅如此，而且还推广了广泛适用的概率均匀连续性（Anscombe）条件，这是另一个看起来根本不像独立条件的条件。我们定义了另一个版本的基本ε无关条件我们证明了它是等价的对于某类随机指标的所有格的随机极限定理，如果度量空间{X γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ是可分离的。在此之后，我们将研究在本研究扩展的随机指标集合中有用停止规则的构造方法。