1999 Fiscal Year Final Research Report Summary
Determinisms of Stable Processes and their Applications
| Project/Area Number |
10640142
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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 | Okayama University Science |
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Principal Investigator |
TAKENAKA Shigeo Okayama Univ. of Sci., Appl. Math., Professor, 理学部, 教授 (80022680)
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| Co-Investigator(Kenkyū-buntansha) |
TAMAMURA Akie Okayama Univ. of Sci., Appl. Math., Professor, 理学部, 教授 (70068914)
TAKASHIMA Keizo Okayama Univ. of Sci., Appl. Math., Professor, 理学部, 教授 (00137184)
WATANABE Hisao Okayama Univ. of Sci., Appl. Math., Professor, 理学部, 教授 (40037677)
KOJO Katuya Niihama Jr. Coll., Dept. Sci. and Math., Lecuturer, 理数科, 講師 (10280471)
IKEDA Takeshi Okayama Univ. of Sci., Appl. Math., Research Assistant, 理学部, 助手 (40309539)
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| Project Period (FY) |
1998 – 1999
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| Keywords | Stable systems / Symmetric stable processes / Determinisms / Integral Geometry / Division number |
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| Research Abstract |
The stable distribution have heavy tails. That is, all of them expect the Gaussian distributions have no variance and some of them have no mean. They are important as models for non-Gaussian (heavy tailed) Phenomena. There exist some examples which have properties called "determinisms". If there exists a natural number n and if for any dimensional distribution higher than n is determined by it n-dimensional marginal distributions, we call that the process has "n-dimensional (weak) determinism".
In this investigation, we have tried to clarify the relation between determinisms and the structure of the process. We get,
1. For a class of processes called set-indexed process, the determinisms are derived from theorems of division numbers in Euclidean Geometry. And for some concrete examples, we obtain the division numbers with proofs.
2. There exist examples of 2 different 2-dimensional stable distributions of which 2-dimensional characteristic functions are coincide inside a sectoral domain.
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