Exit times for an increasing L,vy tree-valued process
成果类型：
Article
署名作者：
Abraham, Romain; Delmas, Jean-Francois; Hoscheit, Patrick
署名单位：
Universite de Orleans; Universite Gustave-Eiffel; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-013-0509-9
发表日期：
2014
页码：
357-403
关键词：
摘要：
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 L,vy 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.
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