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Growing conditioned trees

Author

Listed:
  • Chauvin, Brigitte
  • Rouault, Alain
  • Wakolbinger, Anton

Abstract

For a Markovian branching particle system in d a Palm type distribution on the genealogical trees up to a time horizon t is computed, which generically (i.e. if there are almost surely no multiplicities in the particle positions at time t) can be viewed as a conditional distribution on the trees given that the particle system at time t populates a certain site. The result is obtained in two different ways: by conditioning on the first branching and by means of Kallenberg's method of backward trees.

Suggested Citation

  • Chauvin, Brigitte & Rouault, Alain & Wakolbinger, Anton, 1991. "Growing conditioned trees," Stochastic Processes and their Applications, Elsevier, vol. 39(1), pages 117-130, October.
    • Handle: RePEc:eee:spapps:v:39:y:1991:i:1:p:117-130
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    Citations

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    Cited by:

    1. Shen Lin, 2018. "Typical Behavior of the Harmonic Measure in Critical Galton–Watson Trees with Infinite Variance Offspring Distribution," Journal of Theoretical Probability, Springer, vol. 31(3), pages 1469-1511, September.
    2. Yueyun Hu, 2015. "The Almost Sure Limits of the Minimal Position and the Additive Martingale in a Branching Random Walk," Journal of Theoretical Probability, Springer, vol. 28(2), pages 467-487, June.
    3. Vincent Bansaye, 2019. "Ancestral Lineages and Limit Theorems for Branching Markov Chains in Varying Environment," Journal of Theoretical Probability, Springer, vol. 32(1), pages 249-281, March.
    4. Wilkinson, Richard D. & Tavaré, Simon, 2009. "Estimating primate divergence times by using conditioned birth-and-death processes," Theoretical Population Biology, Elsevier, vol. 75(4), pages 278-285.
    5. Bienvenu, François & Débarre, Florence & Lambert, Amaury, 2019. "The split-and-drift random graph, a null model for speciation," Stochastic Processes and their Applications, Elsevier, vol. 129(6), pages 2010-2048.

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