We study the pruning process developed by Abraham and Delmas (2012) on the discrete Galton–Watson sub-trees of the Lévy tree which are obtained by considering the minimal sub-tree connecting the root and leaves chosen uniformly at rate λ, see Duquesne and Le Gall (2002). The tree-valued...

We study multi-type Bienaymé–Galton–Watson processes with linear-fractional reproduction laws using various analytical tools like the contour process, spinal representation, Perron–Frobenius theorem for countable matrices, and renewal theory. For this special class of branching processes...

Random splitting trees share the striking independence properties of the continuous time binary Galton-Watson tree. They can be represented by Poisson point processes and their contour processes are strong Markov processes. Here we study splitting trees conditioned on extinction, respectively...