2006 Fiscal Year Final Research Report Summary
Integrated Research on The Up-to-Date Problems in Stochastic Numerics
| Project/Area Number |
15340028
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | Ritsumeikan Univ. |
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Principal Investigator |
OGAW Shigeyoshi Ritsumeikan Univ., Dept. of Mathematics, Professor, 理工学部, 教授 (80101137)
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| Co-Investigator(Kenkyū-buntansha) |
MORI Makoto Nihon Univ., Dept. of Humanities and Sci., Professor, 文理学部, 教授 (60092532)
ITO Shunji Kanazawa univ., Graduate School of Sciences, Professor, 自然科学研究科, 教授 (30055321)
NINOMIYA Shoiti Tokyo Inst.of Tech., Graduate School of Management, Professor, マネジメント研究科, 教授 (70313377)
FUKUYAMA Katsushi Kobe Univ., Dept. of Mathematics, Professor, 理学部, 教授 (60218956)
SUGITA Hiroshi Osaka Univ., Graduate School of Sciences, Professor, 理学研究科, 教授 (50192125)
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| Project Period (FY) |
2003 – 2006
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| Keywords | Numerical Solution of the SDE / Stochastic Numerics / Noncausal Stochastic Calculus / Stochastic Solution of Functional Equations / Numerical Integration / Random Numbers / Mathematical Finance |
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| Research Abstract |
The principal aim of this project was to develop the integrated researches on the comteporain problems in stochastic numericas as follows (names in paratheses ( ) are main investigators occupying each session);
(1) Numerical integration by means of Monte Carlo Methods and random numbers (S.Ito, M.Mori, K.Fukuyama, H.Sugita, and S.Ogawa)
(2) Numerical solution of the SDEs (S.Ninomiya and S.Ogawa)
(3) Noncausal calculus based on the Ogawa integral and its applications (S.Ogawa)
(4) Probabilistic solution of functional equations (K.Nishioka, S.Ogawa)
(5) Development of stochastic methods and algorithms for problems in OR, Finance, Computer sciences and Mathematical economy. (S.Ninomiya, K.Nishioka and S.Ogawa)
Through the whole period of the research activity, from 2003 to 2006, each research group cited above has pursuived each research plan, in a pararel way or sometimes in collaboration with other groups and as an integrated research group got many fruitful results not only theoretical but also the results of pratical importance, like the establishment of some computational algorithms in mathematical finance.
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