Fleming-Viot selects the minimal quasi-stationary distribution: The   Galton-Watson case
  Consider N particles moving independently, each one according to a subcritical continuous-time Galton-Watson process unless it hits 0, at which time it jumps instantaneously to the position of one of the other particles chosen uniformly at random. The resulting dynamics is called Fleming-Viot process. We show that for each N there exists a unique invariant measure for the Fleming-Viot process, and that its stationary empirical distribution converges, as N goes to infinity, to the minimal quasi-stationary distribution of the Galton-Watson process conditioned on non-extinction. 
Amine Asselah, Pablo A. Ferrari, Pablo Groisman, Matthieu Jonckheere
math.PR