Breadth first search coding of multitype forests with application to Lamperti representation
Probability
2014-10-02 v1
Abstract
We obtain a bijection between some set of multidimensional sequences and this of -type plane forests which is based on the breadth first search algorithm. This coding sequence is related to the sequence of population sizes indexed by the generations, through a Lamperti type transformation. The same transformation in then obtained in continuous time for multitype branching processes with discrete values. We show that any such process can be obtained from a dimensional compound Poisson process time changed by some integral functional. Our proof bears on the discretisation of branching forests with edge lengths.
Cite
@article{arxiv.1410.0250,
title = {Breadth first search coding of multitype forests with application to Lamperti representation},
author = {Loïc Chaumont},
journal= {arXiv preprint arXiv:1410.0250},
year = {2014}
}