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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


On a formula in diffusion processes in population genetics

Author: Charles J. Holland
Journal: Proc. Amer. Math. Soc. 54 (1976), 316-318
MSC: Primary 60J70; Secondary 92A15
MathSciNet review: 0405609
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Abstract: A problem of recent interest has been the determination of the average values of certain quantities conditioned upon the fixation (or extinction) of the gene in the population. In this note we give another simple proof of formulas for the determination of these quantities.

References [Enhancements On Off] (What's this?)

  • [1] E. B. Dynkin, Markovskie protsessy, Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1963 (Russian). MR 0193670 (33 #1886)
  • [2] W. J. Ewens, Conditional diffusion processes in population genetics, Theoret. Population Biology 4(1973), 21-30.
  • [3] I. I. Gihman and A. V. Skorohod, Stokhasticheskie differentsialnye uravneniya, Izdat. “Naukova Dumka”, Kiev, 1968 (Russian). MR 0263172 (41 #7777)
  • [4] T. Maruyama and M. Kimura, Some methods for treating continuous stochastic processes in population genetics, Japan. J. Genetics 46(1971), 407-410.
  • [5] Thomas Nagylaki, The moments of stochastic integrals and the distribution of sojourn times, Proc. Nat. Acad. Sci. U.S.A. 71 (1974), 746–749. MR 0341637 (49 #6383)

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Additional Information

PII: S 0002-9939(1976)0405609-3
Article copyright: © Copyright 1976 American Mathematical Society

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