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Cycles, permutations and the structure of the yule process with immigration

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  • Joyce, Paul
  • Tavaré, Simon

Abstract

A novel representation of the linear birth process with immigration is analysed. The state space of the process is the collection of permutations of the integers, written in a particular cyclic form. The stochastic structure of the model is particularly simple to describe. The results serve to explain the combinatorial structure of some sampling formulae that arise in the study of neutral mutations in population genetics.

Suggested Citation

  • Joyce, Paul & Tavaré, Simon, 1987. "Cycles, permutations and the structure of the yule process with immigration," Stochastic Processes and their Applications, Elsevier, vol. 25, pages 309-314.
    • Handle: RePEc:eee:spapps:v:25:y:1987:i::p:309-314
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    Cited by:

    1. Arratia, Richard & Barbour, A.D. & Ewens, W.J. & Tavaré, Simon, 2018. "Simulating the component counts of combinatorial structures," Theoretical Population Biology, Elsevier, vol. 122(C), pages 5-11.
    2. Durrett, Richard & Limic, Vlada, 2001. "On the quantity and quality of single nucleotide polymorphisms in the human genome," Stochastic Processes and their Applications, Elsevier, vol. 93(1), pages 1-24, May.

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    Keywords

    linear birth process Yule process;

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