Stochastic Differential Equations and Their Applications

随机微分方程及其应用

• 批准号: 62540150
• 负责人: SHIMIZU Akinobu
• 金额: $ 1.6万
• 依托单位: Nagoya Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1987
• 资助国家: 日本
• 起止时间: 1987 至 1988
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-62540150/
• 关键词: Measure Valued Diffusion; Infinite Allele Model; Multigene Family; Average Identity Probability; ユーンズのサンプリング公式; 無限次元拡散過程; 遺伝モデル; ライト・フィシャーモデル; ユーエンズのサンプリング公式

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.

本研究项目的目的是研究与种群遗传学理论相关的度量值扩散过程。S.N.Ethier和T.S.Kurtz等人对描述群体遗传学中所谓的无限等位基因模型的过程进行了相当多的研究。在这里，我们考虑T.Ohta在1982年提出的描述n轨迹模型的度量值扩散。我们的结果可以总结如下。构造了上述的度量值扩散。导出了三种平均恒等式概率所满足的常微分方程组。这是对Ohta在1982.3获得的结果的数学证明。得到了一种Feens抽样公式，使我们能够在平稳状态下计算随机选择的染色体中的等位基因数目。

项目成果

A.Shimizu: "Nagoya Mathematical Journal".

A.Shimizu：《名古屋数学杂志》。

A.Shimizu: Nagoya Mathematical Journal.

A.Shimizu：名古屋数学杂志。

A.Shimizu: "Measure valued diffusion process describing an n locus model incorporating gene conversion" "Nagoya Mathematical Journal".

A.Shimizu：“测量描述结合基因转换的 n 位点模型的有价值的扩散过程”“名古屋数学杂志”。

Y.Hasegawa: "Brownian motions on infinite dimensional quadratic hypersurfaces" To appear in "Probability Theory and Related Fields".

Y.Hasekawa：“无限维二次超曲面上的布朗运动”出现在“概率论及相关领域”中。

Y.Hasegawa: Theory and Related fields.

Y.Hasekawa：理论和相关领域。