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Direct Product Branching Processes and Related Induced Markoff Chains I. Calculations of Rates of Approach to Homozygosity

  • Samuel Karlin
  • James Mc Gregor

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]).

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References

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    Karlin, S., Direct product branching processes and related Markoff chains, Proc. Nat. Acad. Sci., 51 (1964) 598.Google Scholar
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Copyright information

© Springer-Verlag Berlin Heidelberg 1965

Authors and Affiliations

  • Samuel Karlin
    • 1
  • James Mc Gregor
    • 1
  1. 1.Department of MathematicsStanford UniversityStanfordUSA

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