# 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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https://hal.archives-ouvertes.fr/hal-01070585
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Submitted on : Wednesday, October 1, 2014 - 5:09:08 PM
Last modification on : Wednesday, October 20, 2021 - 3:18:53 AM
Long-term archiving on: : Friday, January 2, 2015 - 11:32:15 AM

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• HAL Id : hal-01070585, version 1

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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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