2000 Fiscal Year Final Research Report Summary
Fleming-Viot Processes with Geographical Structures
| Project/Area Number |
10640130
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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 |
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) |
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, Professor, 経済学部, 教授 (10190620)
MIYAHARA Yoshio Nagoya City University, Faculty of Economics, Professor, 経済学部, 教授 (20106256)
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)
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| Project Period (FY) |
1998 – 2000
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| Keywords | Fleming-Viot Processes / measure valued diffusion / stepping stone model / Markov chain / random discrete distribution / sampling formula |
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| Research Abstract |
(1) Fractional moments of the first passage-times are considered for positively recurrent Markov chains with countable state space. A criterion of the finiteness of the fractional moments is obtained in terms of convergence rate of transition probability to the stationary distribution. As an application it is proved that the passage time of a direct product process has the same order of the fractional moments as that of the single Markov chain.[1]
(2) The stepping stone model with infinite many alleles is studied. The average number of distinct elements in a sample of finite particles in the stationary state of the model is calculated, and the strong-migration-limit of the quantity is discussed.(preprint)
(3) Random discrete probability distributions derived from normalized subordinators are discussed. A generalized Ewens' sampling formula is obtained. The asymptotical behavior of the average length of Young diagrams is made clear in terms of Levy measure.[2]
(4) The average extinction time for a stochastic logistic model is discussed, and its asymptotic behavior is obtaind.(preprint)
(5) The formula of Faa di Bruno is discussed. An elemntary proof of the formila is obtained, and its applications are discussed.[3]
(6) Miyahara obtained many results on geometric Levy processes and minimal martingale measures. He also disccussed its applications to mathernatical finance.[4], [5], [6], [7]
(7) Misawa obtained many results on numerical analysis on stochastic differential equations. He proposed a new method on the analysis. Approximate solutions, in this manner, to a stochastic differential equation preserve conserved quantities of the SDE.
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