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1 results

  • Extinction and explosion of nonlinear Markov branching processes

  • Part of
  • Anthony G. Pakes
  • Journal:
    Journal of the Australian Mathematical Society / Volume 82 / Issue 3 / June 2007
    Published online by Cambridge University Press:
    09 April 2009, pp. 403-428
    Print publication:
    June 2007
    • Article
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  • This paper concerns a generalization of the Markov branching process that preserves the random walk jump chain, but admits arbitrary positive jump rates. Necessary and sufficient conditions are found for regularity, including a generalization of the Harris-Dynkin integral condition when the jump rates are reciprocals of a Hausdorff moment sequence. Behaviour of the expected time to extinction is found, and some asymptotic properties of the explosion time are given for the case where extinction cannot occur. Existence of a unique invariant measure is shown, and conditions found for unique solution of the Forward equations. The ergodicity of a resurrected version is investigated.