Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-14T23:01:50.721Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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