Detection of cellular aging in a Galton-Watson process

Jean-François Delmas (1) , Laurence Marsalle (2)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique
2 LPP - Laboratoire Paul Painlevé - UMR 8524

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.

Mots clés: Aging; Galton-Watson process; bifurcating Markov process; stable convergence

Domaines: Probabilités [math.PR]

Jean-François Delmas, Laurence Marsalle. Detection of cellular aging in a Galton-Watson process. Stochastic Processes and their Applications, 2010, 120 (12), pp.2495-2519. ⟨10.1016/j.spa.2010.07.002⟩. ⟨hal-00293422⟩