| Project/Area Number |
19540140
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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 | Saga University |
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Principal Investigator |
OGURA Yukio Saga University, 理工学部, 非常勤講師 (00037847)
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| Co-Investigator(Kenkyū-buntansha) |
MITOMA Itaru 佐賀大学, 理工学部, 教授 (40112289)
HANDA Kenji 佐賀大学, 理工学部, 准教授 (10238214)
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| Project Period (FY) |
2007 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2007: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 拡散過程 / マルコフ性 / ファジィ集合値確率変数 / 集合係数の確率微分方程式 / 大偏差原理 / Chern-Simons理論 / Poisson-Dirichlet分布 / 中偏差原理 / Chern-Simon摂動展開理論 / 集合値関数の確率積分 / 大数の強法則 / Chern-Simons汎関数 / 確率微分方程式の比較定理 |
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| Research Abstract |
In this study, we first found a lot of new type of stochastic processes in the class of one-dimensional continuous stochastic process with Markov property but without strong Markov property, and moreover determined that class. We then extended strong laws of large numbers and derived large deviation principle for fuzzy set valued random variables. In addition, we proved the existence and uniqueness of solutions almost surely in the space of fuzzy sets (resp. sets) to stochastic differential equations with fuzzy sets (resp. sets) coefficients. We also estimated the term with power 3 integrand in the asymptotic expansion in perturbative Chern-Simons theory. A new characterization of the two-parameter Poisson-Dirichlet distribution was given.
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