  We consider the bifurcating Markov chain model introduced by Guyon to detect
cellular aging from cell lineage. To take into account the possibility for a
cell to die, we use an underlying Galton-Watson process to describe the
evolution of the cell lineage. We give in this more general framework a weak
law of large number, an invariance principle and thus fluctuation results for
the average over one generation or up to one generation. We also prove the
fluctuations over each generation are independent. Then we present the natural
modifications of the tests given by Guyon in cellular aging detection within
the particular case of the auto-regressive model.
