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An indication of the asymptotic nature of the mendelian Markov process

Published online by Cambridge University Press:  14 July 2016

R. G. Khazanie
R. G. Khazanie*
Affiliation:
University of Vermont
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Extract

Consider a finite Markov process {Xn} described by the one-step transition probabilities In describing the transition probabilities in the above manner we are adopting the convention that (0)0 = 1 so that the states 0 and M are absorbing, and the states 1,2,···,M-1 are transient.

Type
Research Papers
Information
Journal of Applied Probability , Volume 5 , Issue 2 , August 1968 , pp. 350 - 356
Copyright
Copyright © Applied Probability Trust 1968 

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References

[1] Fisher, R. A. (1922) On the dominance ratio. Proc. Roy. Soc. 42, 321–341.Google Scholar
[2] Khazanie, R. G. and Mckean, H. E. (1966) A Mendelian Markov process with binomial transition probabilities. Biometrika 53, 37–48.CrossRefGoogle ScholarPubMed
[3] Kimura, M. (1955) Solution of a process of random genetic drift with a continuous model. Proc. Nat. Acad. Sci. USA 41, 144–150.Google Scholar
[4] Malecot, G. (1944) Sur un problème de probabilité en chaîne que pose la génétique. C.R. Acad. Sci. Paris 219, 279–281.Google Scholar
[5] Watterson, G. (1962) Some theoretical aspects of diffusion theory in population genetics. Ann. Math. Statist. 33, 939–957.Google Scholar