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References
J.F. Crow and M. Kimura, An introduction to population genetics theory, Harper and Row, New York, 1970.
S.N.Ethier, An error estimate for the diffusion approximation in population genetics, Ph. D. Thesis, University of Wisconsin, 1975.
S.N. Ethier, A class of degenerate diffusion processes occurring in population genetics, Comm.Pure Appl.Math. 29 (1976), 483–493.
M.I. Freidlin, On the factorization of non-negative definite matrices, Theor. Probability Appl. 13 (1968), 354–356.
J.H. Gillespie, Natural selection for within-generation variance in offspring number, II. Discrete haploid models, Genetics 81 (1975), 403–413.
S. Karlin and J. McGregor, On some stochastic models in genetics, "Stochastic models in medicine and biology" ed. by J. Gurland, Univ. of Wisconsin Press, Madison, 1964, 245–271.
S. Karlin and J. McGregor, Direct product branching processes and related Markov chains, Proc.Nat.Acad.Sci.USA 51 (1964), 598–602.
M. Kimura, Diffusion models in population genetics, J.Appl. Probability 1 (1964), 177–232.
R.A. Littler and E.D. Fackerell, Transition densities for neutral multi-allele diffusion models, Biometrics 31 (1975), 117–123.
N. Okada, On convergence to diffusion processes of Markov chains related to population genetics, (to appear).
K. Sato, Diffusion processes and a class of Markov chains related to population genetics, Osaka J.Math. 13 (1976), 631–659.
K. Sato, A class of Markov chains related to selection in population genetics, J.Math.Soc.Japan 28 (1976), 621–637.
K.Sato, Convergence of a class of Markov chains to mutidimensional degenerate diffusion processes, Proc. Intern.Symp.Stoch.Diff.Eg. (to appear).
K.Sato, Convergence to a diffusion of a multi-allelic model in population genetics, Adv. Appl.Probability (to appear).
N. Shimakura, Equations différentielles provenant de la génétique de population, Tohoku Math.J. 29 (1977), 287–318.
D.W. Stroock and S.R.S. Varadhan, Diffusion processes with continuous coefficients, Comm.Pure Appl.Math. 22 (1969), 345–400 and 479–530.
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Sato, Ki. (1978). Diffusion operators in population genetics and convergence of Markov chains. In: Kallianpur, G., Kölzow, D. (eds) Measure Theory Applications to Stochastic Analysis. Lecture Notes in Mathematics, vol 695. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062660
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DOI: https://doi.org/10.1007/BFb0062660
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