Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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, Markov processes, Fizmatgiz, Moscow, 1963; English transl., Vol. II, Die Grundlehren der math. Wissenschaften, Band 122, Academic Press, New York; Springer-Verlag, Berlin, 1965. MR 33 #1887. 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, Stochastic differential equations, ``Naukova Dumka", Kiev, 1968; English transl., Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 72, Springer-Verlag, Berlin and New York, 1972. MR 41 #7777. 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] T. 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)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 60J70, 92A15

Retrieve articles in all journals with MSC: 60J70, 92A15

Additional Information

Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society