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.