# Breadth first search coding of multitype forests with application to Lamperti representation

Abstract : We obtain a bijection between some set of multidimensional sequences and this of $d$-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 $d^2$ dimensional compound Poisson process time changed by some integral functional. Our proof bears on the discretisation of branching forests with edge lengths.
Keywords :
Type de document :
Pré-publication, Document de travail
2014
Domaine :

Littérature citée [9 références]

https://hal.archives-ouvertes.fr/hal-01070585
Contributeur : Loïc Chaumont <>
Soumis le : mercredi 1 octobre 2014 - 17:09:08
Dernière modification le : mercredi 19 décembre 2018 - 14:08:04
Document(s) archivé(s) le : vendredi 2 janvier 2015 - 11:32:15

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L-Chaumont.pdf
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• HAL Id : hal-01070585, version 1

### Citation

Loïc Chaumont. Breadth first search coding of multitype forests with application to Lamperti representation. 2014. 〈hal-01070585〉

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