Uniform asymptotic independence on essential parts of a sequence of random indices and sufficient conditions of limit theorems with random indices
Project/Area Number  10640144 
Research Category 
GrantinAid for Scientific Research (C).

Section  一般 
Research Field 
General mathematics (including Probability theory/Statistical mathematics)

Research Institution  FUKUOKA UVNIVERSITY 
Principal Investigator 
SUGIMAN Ikuo Fukuoka Univ., Fac. Sci., Assoc. Prof., 理学部, 助教授 (80162890)

CoInvestigator(Kenkyūbuntansha) 
WATANABE Masafumi Fukuoka Univ., Fac. Sci., Prof., 理学部, 教授 (70078559)

Project Fiscal Year 
1998 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥500,000 (Direct Cost : ¥500,000)
Fiscal Year 1999 : ¥500,000 (Direct Cost : ¥500,000)

Keywords  Limit theorem / Stopping rule / Asymptotic independence / Stochastic Processes / 極限定理 / 停止規則 / 漸近的独立性 / 確率過程 / 確率添字 / Anacomba 条件 
Research Abstract 
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 εindependence 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 εindependence 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 εindependence 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. 今後、この範囲の確率添字の束の中から、実用的な停止規則の構成方法を構築することが残る課題といえる。

Report
(4results)
Research Output
(7results)