| Project/Area Number |
21540147
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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 | Nihon University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
陳 蘊剛 東海大学, 生物理工学部, 教授 (50217262)
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| Co-Investigator(Renkei-kenkyūsha) |
ISHIMURA Naoyuki 一橋大学, 大学院・経済学研究科, 教授 (80212934)
IMAI Hitoshi 徳島大学, 大学院・ソシオテクノサイエンス研究部, 教授 (80203298)
MIZUTANI Akira 学習院大学, 理学部, 教授 (80011716)
CHEN Yungang 東海大学, 生物理工学部, 教授 (50217262)
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
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| Keywords | 数理モデル / 相分離 / 金融工学 / Default risk / blow up time / 漸近挙動 / アトラクター / フラクタル次元 / 多倍長計算 / オプション / default-risk system / 極限の可視化 / HWW方程式 / Black-Scholls方程式 |
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| Research Abstract |
We have obtained the following results.1. We showed the effectiveness of the multiple precision arithmetic to approximate the solutions of PDE‘s which have transition phase and the blow up in finite time.2. We derived the default risk model equation and analyze theoretically and numerically.3. We showed the existence and the finite dimensional property of the attractors in magnetic Benard problem4. We applied the multi-precision computation to the equation with delay term,which is hard to compute, and showed that in the case the solution is analytic, it is effective.
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