1988 Fiscal Year Final Research Report Summary
Stochastic Differential Equations and Their Applications
| Project/Area Number |
62540150
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Nagoya Institute of Technology |
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Principal Investigator |
SHIMIZU Akinobu Nagoya Institute of Technology, 工学部, 助教授 (10015547)
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| Co-Investigator(Kenkyū-buntansha) |
KATO Akikuni Nagoya Institute of Technology, 工学部, 助教授 (20024226)
MIWA Megumu Nagoya Institute of Technology, 工学部, 教授 (30011521)
YAMADA Hiroshi Nagoya Institute of Technology, 工学部, 教授 (20022551)
HASEGAWA Yosihei Nagoya Institute of Technology, 工学部, 助教授 (10022675)
YAMAZATO Makoto Nagoya Institute of Technology, 工学部, 助教授 (00015900)
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| Project Period (FY) |
1987 – 1988
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| Keywords | Measure Valued Diffusion / Infinite Allele Model / Multigene Family / Average Identity Probability / ユーンズのサンプリング公式 |
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| Research Abstract |
The aim of this research project is to investigate measure valued diffusion processes related to population genetics theory. The process describing the so-called infinite allele model in population genetics has been rather investigated by S.N.Ethier,T.S.Kurtz and others. Here, we are concerned with the measure valued diffusion describing the n-locus model which was introduced by T.Ohta in 1982.
Our results can be summarized as follows.
1. The measure valued diffusion mentioned above is constructed.
2. The system of ordinary differential equations which the three average identity probabilities satisfy is derived. This is a mathematical justification of the Ohta's results obtained in 1982.
3. A kind of fEens' sampling formula is obtained which enables us to count the number of alleles in a randomly chosen chromosome at stationarity.
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