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 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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Chaumont, L. (2015). Breadth First Search Coding of Multitype Forests with Application to Lamperti Representation. In: Donati-Martin, C., Lejay, A., Rouault, A. (eds) In Memoriam Marc Yor - Séminaire de Probabilités XLVII. Lecture Notes in Mathematics(), vol 2137. Springer, Cham. https://doi.org/10.1007/978-3-319-18585-9_24
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DOI: https://doi.org/10.1007/978-3-319-18585-9_24
Publisher Name: Springer, Cham
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