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Bull. Korean Math. Soc. 2003; 40(4): 677-683
Printed December 1, 2003
Copyright © The Korean Mathematical Society.
The application of stochastic differential equations to population genetic model
Won Choi and Dug-Hwan Choi
University of Incheon, University of Incheon
In multi-allelic model $X=(x_1 ,x_2 ,\cdots ,x_d )$, \[ M_f(t)=f(p(t))-\int_0^t Lf(p(t))ds \] is a $P$-martingale for diffusion operator $L$ under the certain conditions. In this note, we examine the stochastic differential equation for model $X$ and find the properties using stochastic differential equation.
Keywords: allelic model, martingale problem, stochastic differential equation, random genetic drift, mutation rate, natural selection
MSC numbers: 92D10, 60H30, 60G44
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