2005 Fiscal Year Final Research Report Summary
Lie algebra & group methods to non-linear stochastic dynamical systems and its applications
| Project/Area Number |
14540133
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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 | Nagoya City University |
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Principal Investigator |
MISAWA Tetsuya Nagoya City University, Graduate School of Economics, Prof., 大学院・経済学研究科, 教授 (10190620)
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| Co-Investigator(Kenkyū-buntansha) |
MIYAHARA Yoshio Nagoya City University, Graduate School of Economics, Prof., 大学院・経済学研究科, 教授 (20106256)
SHIMIZU Akinobu Nagoya City University, Graduate School of Natural Sciences, Visiting Prof., 大学院・システム自然科学研究科, 客員教授 (10015547)
NOTOHARA Morihiro Nagoya City University, Graduate School of Natural Sciences, Associate Prof., 大学院・システム自然科学研究科, 助教授 (30347421)
HASHIMOTO Yoshiaki Nagoya City University, Graduate School of Natural Sciences, Prof., 大学院・システム自然科学研究科, 教授 (50106259)
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| Project Period (FY) |
2002 – 2005
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| Keywords | Stochastic dynamical systems / Composition methods / Mathematical finance / Geometric Levy processes / Population genetics / Coalescent model, / Geographical structure / Gevrey hypoellipticity |
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| Research Abstract |
The present study focuses on Lie algebra & group methods to formulate numerical schemes of stochastic differential equations and the related topics on non-linear stochastic dynamical systems governed by such stochastic equations.
The head investigator, Misawa, deeply investigates "symplectic integrators" for stochastic Hamiltonian dynamical systems by using "composition methods"which are formulated on the basis of Lie algebra & group theory. The new schemes are advantageous to preserve symplectic structure of the stochastic Hamiltonian systems numerically and are useful for producing the stable numerical solutions. To examine the superiority, Misawa also gives an illustrative example on the proposed schemes for such stochastic systems.
In order to investigate the utility of stochastic numerical analysis, the investigators study on non-linear stochastic dynamical systems in various research fields. Misawa studies numerical simulations of stochastic macroeconomic models, Markov chain algor
… More
ithm in smoothing time series data and stochastic and statistical models in financial engineering. Particularly, he mainly works with investigating some regression models concerning with electricity markets. The investigator, Miyahara, studies the option pricing problems in the incomplete asset market, which is one of the important problems in the field of mathematical finance. He also constructs the [Geometric Levy process & MEMM] pricing model, in which the geometric Levy processes are adopted as the underlying asset price processes and the MEMM(=minimal entropy martingale measure), and investigates the properties of this model. The investigator, Shimizu, works with the following topics ; coalescent process with fluctuating population size and its effective population size, Poisson random measures and infinitely divisible distributions in population genetics, and the Handa model incorporating symmetric selections. The investigator, Notohara studies the genealogy of sampled genes from geographically structured population which is described by a Markov process called Structured Coalescent Model. He investigates effects of the geographical structure on the distribution of the coalescence time, which is the time to the most recent common ancestor of samples, and the distribution of the number of segregating sites detected in sampled DNA sequences. The investigator, Hashimoto, studies non-isotropic Gevrey hypoellipticity for Grushin operators and the analyticity of the solutions of the non-linear elliptic partial differential equations. Through these related topics, we find out that stochastic dynamical theory and stochastic numerical methods are useful for the analysis of the several stochastic models. Less
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Research Products
(60 results)
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[Book] バイオインフォマティクス事典2006
Author(s)
編集委員:宮野悟, 江口至洋, 金久實, 高木利久, 中井謙太, 分担執筆者・含, 能登原盛弘
Publisher
共立出版(東京)(出版予定)
Description
「研究成果報告書概要(和文)」より
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