Exit times for an increasing Lévy tree-valued process

  title={Exit times for an increasing L{\'e}vy tree-valued process},
  author={Jean-François Delmas and Patrick Hoscheit},
We give an explicit construction of the increasing tree-valued process introduced by Abraham and Delmas using a random point process of trees and a grafting procedure. This random point process will be used in companion papers to study record processes on Lévy trees. We use the Poissonian structure of the jumps of the increasing tree-valued process to describe its behavior at the first time the tree grows higher than a given height. We also give the joint distribution of this exit time and the… CONTINUE READING