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Direct Product Branching Processes and Related Induced Markoff Chains

I. Calculations of Rates of Approach to Homozygosity

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Bernoulli 1713 Bayes 1763 Laplace 1813

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Abstract

In this paper we introduce a class of finite state Markoff chains of special structure which includes many cases of interest in applications. For these chains we will determine a full set of eigenvalues (Sections 3 and 4) and provide their probabilistic interpretations (Section 5) which in the present context is rather striking. An intrinsic characterization of these processes and some associated limit theorems will be elaborated in a separate publication (see also [4]).

Prepared under Auspices of National Institutes of Health GM 10452-01 A 1.

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References

  1. Feller, W.: Diffusion processes in genetics. Proc. 2nd Berkeley Symp. Mathematical Statistics and Probability. University of California Press 1951, p. 227.

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  4. Karlin, S., and J. McGregor: Direct product branching processes and related Markoff chains, Proc. Nat. Acad. Sci., 51 (1964) 598.

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Authors and Affiliations

  1. Department of Mathematics, Stanford University, Stanford, California, USA

    Samuel Karlin & James Mc Gregor

Authors
  1. Samuel Karlin
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  2. James Mc Gregor
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Editor information

Jerzy Neyman Lucien M. Le Cam

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© 1965 Springer-Verlag Berlin Heidelberg

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Karlin, S., Mc Gregor, J. (1965). Direct Product Branching Processes and Related Induced Markoff Chains. In: Neyman, J., Le Cam, L.M. (eds) Bernoulli 1713 Bayes 1763 Laplace 1813. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-49750-6_8

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  • DOI: https://doi.org/10.1007/978-3-642-49750-6_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-49467-3

  • Online ISBN: 978-3-642-49750-6

  • eBook Packages: Springer Book Archive

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