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ON THE DIFFUSION OPERATOR IN POPULATION GENETICS

  • Choi, Won (Department of Mathematics, University of Incheon)
  • 투고 : 2011.08.01
  • 심사 : 2011.09.26
  • 발행 : 2012.05.30

초록

W.Choi([1]) obtains a complete description of ergodic property and several property by making use of the semigroup method. In this note, we shall consider separately the martingale problems for two operators A and B as a detail decomposition of operator L. A key point is that the (K, L, $p$)-martingale problem in population genetics model is related to diffusion processes, so we begin with some a priori estimates and we shall show existence of contraction semigroup {$T_t$} associated with decomposition operator A.

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참고문헌

  1. W.Choi and B.K.Lee On the diffusion processes and their applications in population genetics, J. Applied Mathematics and Computing, Vol 15, No 1-2 (2004), 415-423
  2. S.N.Either, A class of degenerate diffusion processes occurring in population genetics, Comm. Pure Appl. Math., 29 (1976), 483-493. https://doi.org/10.1002/cpa.3160290503
  3. S.N.Either, A class of infinite dimensional diffusions occurring in population genetics, Indiana Univ. J., 30 (1981), 925-935. https://doi.org/10.1512/iumj.1981.30.30068
  4. J.H.Gillespie, Natural selection for within-generation variance in offspring number, Genetics, 76 (1974), 601-606.
  5. N.Okada, On the uniqueness problem of two dimensional diffusion processes occurring in population genetics, Z.Wahr.Verw.Geb., 56 (1981), 63-74. https://doi.org/10.1007/BF00531974