Infinite dimensional stochastic differential equations and their applications
Infinite dimensional stochastic differential equations and their applications
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无限维随机微分方程及其应用
DOI：
10.1215/kjm/1250522207
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发表时间：
1980
影响因子：
--
通讯作者：
A. Shimizu
中科院分区：
文献类型：
--
作者：
T. Shiga;A. Shimizu
本文的中心目的是通过建立无限维随机微分方程，构造与种群遗传学或统计力学有关的几类无限维随机过程。例如，在人口遗传学中，我们将会有一个新的经验。L和S是可数的S和S在一起的殖民地。假设每个群体有两个等位基因A和a，基因频率的变化是由随机抽样、突变、选择和迁移引起的。A S是著名的群体遗传学S a L]，[6])，当忽略迁移效应时，A基因在同一区域的频率xi(T)可被认为是由扩散系数决定的在区间[0，1]上一维扩散过程的路径
The central aim o f this paper is to construct som e classes o f infinite dimensional stochastic processes related to population genetics or statistical m echanics by m aking u s e o f infinite dimensional stochastic differential equations. T o b eg in w ith , w e w ill exp la in a n e x a m p le r e la te d to population gen etics . L et S b e a countable s e t w h ich w e co n sid er a s th e se t o f colonies. Suppose that there are two alleles A and a in each colony and th a t th e ch an g e o f gene frequencies is caused by random sam p ling , mutation, selection and m igration . A s is well-known in population genet ic s a l ] , [6 ] ) , w h e n w e ignore the m igration effect, the frequency x i (t) of A-genes in th e ith co lo n y a t t im e t m ay be considered a path of 1-dimensional diffusion process on the in terval [0 , 1 ] determ ined by the diffusion coefficient