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

Loïc Chaumont (1)

1 LAREMA - Laboratoire Angevin de Recherche en Mathématiques

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.

Mots clés: Lamperti representation; compound Poisson process; multitype branching forests; breadth first search coding; random walks

Domaines: Probabilités [math.PR]

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