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

• 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

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.

在这项研究中，我们研究了 {XiiD2τnieD2} 的（随机）极限定理的充分条件的推广，其中 {XiiD2τnieD2} 是度量空间的随机元素的格子，而 {τD2D2} 是随机多维索引的格子。我们定义{XD2D2} 的基本 ε 独立条件{τiiD2niieD2} 作为均匀渐进独立条件的广义版本，并在本研究中给出了该条件的随机极限定理。这些条件和结果是均匀 ε 独立条件和该条件的随机极限定理的推广。 ，我们证明这些不仅如此，而且是广泛适用的概率一致连续性（Anscombe）条件的概括，并且是另一个条件看起来不像独立条件我们定义了基本 ε 独立条件的另一个版本，并且我们证明，如果度量空间 { } 的值为，则它等效于某个类的所有随机索引格的随机极限定理。之后，我们将研究在本研究中扩展的随机指标集中有用的停止规则的构造方法。

项目成果

Ikuo Sugiman: "Asymptotic ε-independence on essential parts of random indices and the limit theorems of randomly indexed sequences of random elements of separable metric space" RIMS Kokyuroku. (印刷中). (1999)

Ikuo Sugiman：“随机索引基本部分的渐近 ε 独立性和可分离度量空间随机元素随机索引序列的极限定理”RIMS Kokyuroku（出版中）。

Ikuo Sugiman: "Uniform Independence on Essential Parts of Random Indices and the Limit Therem of Randomly Indexed Sequences"Fukuoka Univ.Sci.Reports. 30(1). 85-91 (2000)

杉万育夫：“随机索引基本部分的一致独立性和随机索引序列的极限定理”福冈大学科学报告。

Ikuo Sugiman: "Uniform Independence on Essential Parts of Random Indices and the Limit Theorem of Randomly Indexed Sequences"Fukuoka Univ. Sci. Reports. 30(1). 85-91 (2000)

杉满郁夫：《随机索引基本部分的一致独立性和随机索引序列的极限定理》福冈大学

Masafumi Watanabe: "Strong consistency for a modified RM stochastic approximation algorithm without assuming the boundedness condition"Fukuoka Univ. Sci. Reports. 29(1). 47-62 (1999)

Masafumi Watanabe：“在不假设有界条件的情况下，改进的 RM 随机逼近算法的强一致性”福冈大学。

Masafumi Watanabe: "Strong consistency for a modified RM stochastic approximation algorithm without assuming the boundedness condition"Fukuoka Univ.Sci.Reports. 29(1). 47-62 (1999)

Masafumi Watanabe：“在不假设有界条件的情况下，改进的 RM 随机逼近算法的强一致性”福冈大学科学报告。