2000 Fiscal Year Final Research Report Summary
Analysis of Infinite-dimensional Markovian Models
| Project/Area Number |
11640103
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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 | Tokyo Institute of Technology |
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Principal Investigator |
SHIGA Tokuzo Graduate School of Science and Engineering, Tokyo Institute of Technology Professor, 大学院・理工学研究科, 教授 (60025418)
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| Co-Investigator(Kenkyū-buntansha) |
SHIRAI Tomoyuki Graduate School of Science and Engineering, Tokyo Institute of Technology Assistant, 大学院・理工学研究科, 助手 (70302932)
MURATA Minoru Graduate School of Science and Engineering, Tokyo Institute of Technology Professor, 大学院・理工学研究科, 教授 (50087079)
MORITA Takehiko Graduate School of Science and Engineering, Tokyo Institute of Technology Associate Professor, 大学院・理工学研究科, 助教授 (00192782)
MINAMI Nariyuki Institute of Mathematics, University of Tsukuba, Associate Professor, 数学系, 助教授 (10183964)
SUMI Hiroki Graduate School of Science and Engineering, Tokyo Institute of Technology Assistant, 大学院・理工学研究科, 助手 (40313324)
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| Project Period (FY) |
1999 – 2000
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| Keywords | measure-valued diffusion / Fleming-Viot process / time reversibility / interacting diffusion / random potential |
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| Research Abstract |
We performed this project and obtained the following results. 1. Fleming-Viot proccesess form an important class of measure-valued Markov processes and well-applied as basic models to population genetics. Concerning these we resolved an open problem to determine the situation that the Fleming-Viot processes have time reversible stationary distribution. 2. In the case that selective intensity is unbounded we proved well-posedness of the processes and uniqueness of stationary distribution. This problem is much harder than the bounded selection case. 3. Interacting diffusion systems form an important class of the theory of interacting Markov processes, which have been well developed when the noises are spatially independent. We considered spatially correlated noises, and obtained some ergodic results. 4. Heat equation with Gausian white noise potential defines a function-valued diffusion, which is important from a view point of random polymer model. For this equation we developed asymptotic analysis of moments of the solution.
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