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2 results

  • Uniqueness of Quasistationary Distributions and Discrete Spectra when ∞ is an Entrance Boundary and 0 is Singular

  • Part of
  • Jorge Littin C.
  • Journal:
    Journal of Applied Probability / Volume 49 / Issue 3 / September 2012
    Published online by Cambridge University Press:
    04 February 2016, pp. 719-730
    Print publication:
    September 2012
    • Article
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  • We study quasistationary distributions on a drifted Brownian motion killed at 0, when +∞ is an entrance boundary and 0 is an exit boundary. We prove the existence of a unique quasistationary distribution and of the Yaglom limit.

  • On the genealogy of large populations

  • J. F. C. Kingman
  • Journal:
    Journal of Applied Probability / Volume 19 / Issue A / 1982
    Published online by Cambridge University Press:
    14 July 2016, pp. 27-43
    Print publication:
    1982

  • A new Markov chain is introduced which can be used to describe the family relationships among n individuals drawn from a particular generation of a large haploid population. The properties of this process can be studied, simultaneously for all n, by coupling techniques. Recent results in neutral mutation theory are seen as consequences of the genealogy described by the chain.