| Project/Area Number |
10640144
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | FUKUOKA UVNIVERSITY |
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Principal Investigator |
SUGIMAN Ikuo Fukuoka Univ., Fac. Sci., Assoc. Prof., 理学部, 助教授 (80162890)
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| Co-Investigator(Kenkyū-buntansha) |
WATANABE Masafumi Fukuoka Univ., Fac. Sci., Prof., 理学部, 教授 (70078559)
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| Project Period (FY) |
1998 – 1999
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| Project Status |
Completed (Fiscal Year 1999)
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| Budget Amount *help |
¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1999: ¥500,000 (Direct Cost: ¥500,000)
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| Keywords | Limit theorem / Stopping rule / Asymptotic independence / Stochastic Processes / 確率添字 / Anacomba 条件 |
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| 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 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.
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