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The forest associated with the record process on a Lévy tree

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  • Abraham, Romain
  • Delmas, Jean-François

Abstract

We perform a pruning procedure on a Lévy tree and instead of throwing away the removed sub-tree, we regraft it on a given branch (not related to the Lévy tree). We prove that the tree constructed by regrafting is distributed as the original Lévy tree, generalizing a result of Addario-Berry, Broutin and Holmgren where only Aldous’s tree is considered. As a consequence, we obtain that the “average pruning time” of a leaf is distributed as the height of a leaf picked at random in the Lévy tree.

Suggested Citation

  • Abraham, Romain & Delmas, Jean-François, 2013. "The forest associated with the record process on a Lévy tree," Stochastic Processes and their Applications, Elsevier, vol. 123(9), pages 3497-3517.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:9:p:3497-3517
    DOI: 10.1016/j.spa.2013.04.017
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    References listed on IDEAS

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    1. Delmas, Jean-François, 2007. "Fragmentation at height associated with Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 117(3), pages 297-311, March.
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