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3 results

  • The neutral two-locus model as a measure-valued diffusion

  • S. N. Ethier, R. C. Griffiths
  • Journal:
    Advances in Applied Probability / Volume 22 / Issue 4 / December 1990
    Published online by Cambridge University Press:
    01 July 2016, pp. 773-786
    Print publication:
    December 1990

  • The neutral two-locus model in population genetics is reformulated as a measure-valued diffusion process and is shown under certain conditions to have a unique stationary distribution and be weakly ergodic. The limits of the process and its stationary distribution as the recombination parameter tends to infinity are found. Genealogies are incorporated into the model, and it is shown that a random sample of size n from the population at stationarity has a common ancestor.

  • Finite non-homogeneous Markov chains: Asymptotic behaviour

  • Harry Cohn
  • Journal:
    Advances in Applied Probability / Volume 8 / Issue 3 / September 1976
    Published online by Cambridge University Press:
    01 July 2016, pp. 502-516
    Print publication:
    September 1976

  • The paper is concerned with aspects of the behaviour of the products of finite stochastic matrices, the methods used in the proofs being of a probabilistic nature. The main result of the paper (Theorem 1) presents a general picture of the asymptotic behaviour of the transition probabilities between various groups of states. A unified treatment of some results of non-homogeneous Markov chain theory pertaining to weak ergodicity is then given.