| Project/Area Number |
24340022
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Partial Multi-year Fund |
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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 | Ritsumeikan University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
AKAHORI Jiro 立命館大学, 理工学部, 教授 (50309100)
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| Co-Investigator(Renkei-kenkyūsha) |
NINOMIYA Syoichi 東京工業大学, 大学院イノベーションマネジメント研究科, 教授 (70313377)
KUSUOKA Shigeo 東京大学, 理学部, 教授 (00114463)
TAKEUCHI Atsushi 大阪市立大学, 理学部, 准教授 (30336755)
HAYASHI Masafumi 琉球大学, 理学部, 助教 (90532549)
YASUDA Kazuhiro 法政大学, 理工学部, 准教授 (80509638)
NAKATSU Tomonori 立命館大学, 理工学部, 助教 (50732898)
TANAKA Hideyuki 立命館大学, 理工学部, 助教 (20732895)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥9,230,000 (Direct Cost: ¥7,100,000、Indirect Cost: ¥2,130,000)
Fiscal Year 2014: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2013: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2012: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
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| Keywords | 確率過程 / シミュレーション / 数値解析 / 無限次元解析 / 確率微分方程式 / ジャンプ型モデル / Malliavin解析 / 確率変数 / Multi-levelモンテカルロ方法 / 密度関数 / BSDE / 近似 |
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| Outline of Final Research Achievements |
Stochastic differential equations (sde's) are used in various applied sciences as dynamic random models. Using these models different results are explained and measured. From the theoretical point of view, various results have been achieved through the years. But in order to make these results applicable in practice one needs to perform Monte Carlo simulations. The present project was developed in this setting and in particular we deal with sde's with non-smooth coefficients. We have developed tools in order to perform numerical simulations and analysis of the methods proposed. In the present world, due to rapid changes of dynamics, one sees that the change in model parameters is sudden and therefore the usual models which use smooth coefficients are not sufficient to handle the demand from applications. That is usual methods which apply to smooth cases do not perform well in the irregular case and therefore one needs to develop new tools. This was the goal of the present project.
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