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THE APPLICATION OF STOCHASTIC DIFFERENTIAL EQUATIONS TO POPULATION GENETIC MODEL

  • Choi, Won (Department of Mathematics, University of Incheon) ;
  • Choi, Dug-Hwan (Department of Mathematics, University of Incheon)
  • Published : 2003.11.01

Abstract

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.

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Cited by

  1. Derivation of Several SDE Systems in One- and Two-Locus Population Genetics vol.32, pp.5, 2014, https://doi.org/10.1080/07362994.2014.922030
  2. ON THE MARTINGALE PROPERTY OF LIMITING DIFFUSION IN SPECIAL DIPLOID MODEL vol.31, pp.1_2, 2013, https://doi.org/10.14317/jami.2013.241