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arXiv · 1410.0250

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

Loïc Chaumont
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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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Loïc Chaumont. 2014-10-01. Breadth first search coding of multitype forests with application to Lamperti representation. https://arxiv.org/abs/1410.0250

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