Breadth First Search Coding of Multitype Forests with Application to Lamperti Representation

Abstract

We obtain a bijection between some set of multidimensional sequences and the set 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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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.LAREMA – UMR CNRS 6093, Université d’AngersAngers Cedex 01France

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