Non regular limits of one-dimensional generalized diffusion processes

一维广义扩散过程的非正则极限

• 批准号: 22540132
• 负责人: TOMISAKI Matsuyo
• 金额: $ 2.41万
• 依托单位: Nara Women's University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22540132/
• 关键词: 広義拡散過程; 双一般化拡散過程; 出生死滅過程; モラン・モデル; 調和変換; レヴィ測度; モランモデル; 条件付き確率過程; マルコフ性

We considered the phenomena where we have non regular limits of one-dimensional generalized diffusion processes. When the limit of scale functions and that of speed measure functions have common discontinuous points, we proved the convergence of transition probabilities and showed that the limit process can be a one-dimensional bi-generalized diffusion process, by means of convergence of Green functions. We also investigated the effect of boundary conditions on harmonic transform of one-dimensional generalized diffusion processes. Further we showed some limit theorems for Moran model in population genetics.

我们考虑了一维广义扩散过程具有不规则极限的现象。当尺度函数的极限与速度测度函数的极限具有共同的不连续点时，利用格林函数的收敛性证明了过渡概率的收敛性，并证明了极限过程可以是一维双广义扩散过程。研究了边界条件对一维广义扩散过程谐波变换的影响。进一步给出了群体遗传学中Moran模型的极限定理。

项目成果

The effects of back mutation on compensatory molecular evolution

回复突变对补偿性分子进化的影响

• 发表时间: 2012
• 作者: M.Kuwamura;K.Maeda;T.Adachi-Yamada;M. Tomisaki;桑村雅隆;M.Iizuka;桑村雅隆;T.Takemura and M.Tomisaki;桑村雅隆;T.Takemura and M.Tomisaki;桑村雅隆;M.Iizuka
• 通讯作者: M.Iizuka

Minkowski の定理の一般化(1950, H. P. Mulholland) に関する話題

与闵可夫斯基定理推广相关的主题（1950，H. P. Mulholland）

• 作者: Saeki;Yusuke; Kuroiwa;Daishi;Y. Moritoh
• 通讯作者: Y. Moritoh

Weak mutation limits of the Moran model in population genetics

群体遗传学中莫兰模型的弱突变限制

• 发表时间: 2013
• 期刊: Ann. Reports of Graduate School of Humanities and Sciences, Nara Women’s University
• 作者: M. Tomisaki and M. Iizuka;M. Tomisaki and M. Iizuka
• 通讯作者: M. Tomisaki and M. Iizuka

Intrinsic ultracontractivity and semismall perturbations for skew product diffusion operators

斜积扩散算子的本征超收缩性和半小扰动

• 发表时间: 2013
• 作者: M.Kuwamura;K.Maeda;T.Adachi-Yamada;M. Tomisaki
• 通讯作者: M. Tomisaki

Levy measure density corresponding to inverse local time

Levy 测量与本地时间倒数对应的密度

• 发表时间: 2012
• 作者: M.Kuwamura;K.Maeda;T.Adachi-Yamada;M. Tomisaki;桑村雅隆;M.Iizuka;桑村雅隆;T.Takemura and M.Tomisaki
• 通讯作者: T.Takemura and M.Tomisaki