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

2014/10/01 by Loïc Chaumont, Chaumont, Loïc
Mathematics · #60C05 #60J80 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60C05 #msc:60J80

paper · pdf · doi:10.48550/arxiv.1410.0250

arxiv created 2014/10/01 · arxiv updated 2014/10/02

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 d² 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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