| Project/Area Number |
08640260
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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 (1997)
Yokohama National University (1996) |
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Principal Investigator |
SHIMIZU Akinobu Nagoya City University, Institute of Natural Sciences, Professor, 自然科学研究教育センター, 教授 (10015547)
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| Co-Investigator(Kenkyū-buntansha) |
HASHIMOTO Yoshiaki Nagoya City University, Institute of Natural Sciences.Professor, 自然科学研究教育センター, 教授 (50106259)
OKUTO Yuji Nagoya City University, Institute of Natural Sciences, Professor, 自然科学研究教育センター, 教授 (80295625)
MISAWA Tetsuya Nagoya City University, Faculty of Economics, Associate Professor, 経済学部, 助教授 (10190620)
MIYAHARA Yoshio Nagoya City University, Faculty of Economics, Professor, 経済学部, 教授 (20106256)
KONNO Norio Yokohama National University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (80205575)
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| Project Period (FY) |
1996 – 1997
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| Keywords | measure-valued diffusion / infinite site model / stepping stone model / genealogy / infinite allele model / population genetics |
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| Research Abstract |
The head investigator has investigated a genealogical problem of a stepping stone Fleming-Viot process. He got the following results : The average probability that two genes randomly chosen in the stationary state of the diffusion have a common ancestor is written in the term of the coalescent time of the dual process. Assume that the set of colonies is the d-dimensional lattice, and that the migration process is a random walk. Then, in order that the two genes have a common ancestor with probability 1, it is necessary and sufficient that the dimension d is less than or equal to 2. The average probability that the number of all mutations since the common anscestor equals s is given by a mixture of Poisson distributions.
Next, the head investigator has investigated the number of alleles in a sample of finite genes for stepping stone models with infinitely many alleles. His motivation is to try to extend the well-known results in the case without geographical structure for stepping stone models. This is a joint work with T.Soshi.
The investigator, N.Konno, has investigated infinite particle systems. He got many results in mathematical aspects and applied fields. The investigator, Y.Miyahara has investigated canonical martingale measures related to incomplete assets markets. The investigator, T.Misawa, has investigated stochastic dynamical systems. He got conserved quantities observing symmetry of dynamical systems.
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