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.
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Pré-publication, Document de travail
2014
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https://hal.archives-ouvertes.fr/hal-01070585
Contributeur : Loïc Chaumont <>
Soumis le : mercredi 1 octobre 2014 - 17:09:08
Dernière modification le : lundi 5 février 2018 - 15:00:03
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Loïc Chaumont. Breadth first search coding of multitype forests with application to Lamperti representation. 2014. 〈hal-01070585〉

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