HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

Exit times for an increasing Lévy tree-valued process

Abstract : 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, using a spinal decomposition of the tree, similar to the classical Bismut and Williams decompositions. We also give the joint distribution of this exit time and the ascension time which corresponds to the first infinite jump of the tree-valued process.
Document type :
Journal articles
Complete list of metadata

Cited literature [24 references]  Display  Hide  Download

Contributor : Patrick Hoscheit Connect in order to contact the contributor
Submitted on : Friday, April 24, 2015 - 4:22:18 PM
Last modification on : Tuesday, October 12, 2021 - 5:20:12 PM
Long-term archiving on: : Wednesday, April 19, 2017 - 5:59:21 AM


Files produced by the author(s)




Romain Abraham, Jean-François Delmas, Patrick Hoscheit. Exit times for an increasing Lévy tree-valued process. Probability Theory and Related Fields, Springer Verlag, 2014, 159 (1-2), pp.357-403. ⟨10.1007/s00440-013-0509-9⟩. ⟨hal-00673870v2⟩



Record views


Files downloads