A class of Markov chains related to selection in polulation genetics

Ken-iti SATO

doi:10.2969/jmsj/02840621

Ken-iti SATO

Author information

JOURNAL FREE ACCESS

1976 Volume 28 Issue 4 Pages 621-637

DOI https://doi.org/10.2969/jmsj/02840621

Details

Published: 1976 Received: August 07, 1975 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
Correction information
Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) J. F. Crow and M. Kimura, An introduction to population genetics theory, Harper and Row, New York, 1970.
2) S. Karlin, A first course in stochastic processes, Academic Press, New York, 1966.
3) S. Karlin and J. McGregor, Direct product branching processes and related Markov chains, Proc. Nat. Acad. Sci. USA, 51 (1964), 598-602.
4) H. J. Kushner, On the weak convergence of interpolated Markov chains to a diffusion, Ann. Probability, 2 (1974), 40-50.
5) K. Sato, Asymptotic properties of eigenvalues of a class of Markov chains induced by direct product branching processes, J. Math. Soc. Japan, 28 (1976), 192-211.
6) K. Sato, Diffusion processes and a class of Markov chains related to population genetics, Osaka J. Math., to appear.
7) D.W. Stroock and S.R.S. Varadhan, Diffusion processes with continuous coefficients, I, Comm. Pure Appl. Math., 22 (1969), 345-400; II, Comm. Pure Appl. Math., 479-530.
8) T. Yamada and S. Watanabe, On the uniqueness of solutions of stochastic differential equations, J. Math. Kyoto Univ., 11 (1971), 155-167; II, Math. Kyoto Univ., 553-563.

Right : [1] J. F. Crow and M. Kimura, An introduction to population genetics theory, Harper and Row, New York, 1970.
[2] S. Karlin, A first course in stochastic processes, Academic Press, New York, 1966.
[3] S. Karlin and J. McGregor, Direct product branching processes and related Markov chains, Proc. Nat. Acad. Sci. USA, 51 (1964), 598-602.
[4] H. J. Kushner, On the weak convergence of interpolated Markov chains to a diffusion, Ann. Probability, 2 (1974), 40-50.
[5] K. Sato, Asymptotic properties of eigenvalues of a class of Markov chains induced by direct product branching processes, J. Math. Soc. Japan, 28 (1976), 192-211.
[6] K. Sato, Diffusion processes and a class of Markov chains related to population genetics, Osaka J. Math., to appear.
[7] D. W. Stroock and S. R. S. Varadhan, Diffusion processes with continuous coefficients, I, Comm. Pure Appl. Math., 22 (1969), 345-400; II, Comm. Pure Appl. Math., 479-530.
[8] T. Yamada and S. Watanabe, On the uniqueness of solutions of stochastic differential equations, J. Math. Kyoto Univ., 11 (1971), 155-167; II, J. Math. Kyoto Univ., 553-563.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

Corresponding author

Correction information

Register with J-STAGE for free!