| Project/Area Number |
21540133
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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 University of Education |
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Principal Investigator |
NAKATA Toshio 福岡教育大学, 教育学部, 教授 (10304693)
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| Co-Investigator(Kenkyū-buntansha) |
TAMARI Fumikazu 福岡教育大学, 教育学部, 名誉教授 (70036937)
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| Co-Investigator(Renkei-kenkyūsha) |
KUBO Izumi 広島大学, 理学研究科, 名誉教授 (70022621)
IKEDA Satoshi 宮崎大学, 工学部, 准教授 (70282796)
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| Project Period (FY) |
2009-04-01 – 2014-03-31
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 離散確率モデル / ポアソンの小数の法則 / 大数の法則 / 中心極限定理 / ネックレス過程 / フェラーのゲーム / 切断和 / 切断確率変数 / 重い裾 / ペテルスブルグのゲーム / 単純ランダムウォーク / 安定分布 / 正則変動 / Schur凸性 / 衝突確率 / 占有問題 / 玉と壷のモデル / Chen-Steinの方法 / ボルツマン抽出 / ボアソンの小数の法則 / 大数の弱法則 / 大数の強法則 / ポアソン近似 |
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| Research Abstract |
In this research, motivated by analysis of algorithms, we study discrete probability models. Specifically, they mainly contains three topics, namely, "balls and urns with collisions", "necklace processes", and "Feller game and related topics", and we investigate finite structures and limit distributions. For each discrete probability model, we extend known results, and have some limit theorems. Thereby, it seems that the stochastic phenomena of the models may be just solved.
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