Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지

ON THE DIFFUSION PROCESSES AND THEIR APPLICATIONS IN POPULATION GENETICS

  • Choi, Won (Department of Mathematics, University of Incheon) ;
  • Lee, Byung-Kwon (Department of mathematics, University of Incheon)
  • Published : 2004.05.01

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Abstract

In allelic model X = ($x_1,\;x_2,...x_{d}$), $M_f(t)$= f(p(t)) - ${{\int}^{t}}_0$Lf(p(t))ds is a P-martingale for diffusion operator L under the certain conditions. In this note, we can show uniqueness of martingale problem associated with mean vector and obtain a complete description of ergodic property by using of the semigroup method.

Keywords

References

  1. The application of diffusion processes to population genetic model W. Choi
  2. Comm. Pure Appl. Math. v.29 A class of degenerate diffusion processes occurring in population genetics S. N. Ethier
  3. Indiana Univ. J. v.30 A class of infinite dimensional diffusions occurring in population genetics S. N. Ethier
  4. Genetics v.76 Natural selection for within-generation variance in offspring number J.H.Gillespie
  5. Z. Wahr. Verw. Geb. v.56 On the uniqueness problem of two dimensional diffusion processes occurring in population genetics N. Okada
  6. Continuous martingales and Broumian motion D.Revuz;M.Yor
  7. Theory of population genetics and evolutionary ecology:An Introduction J. Rougharden