Quasi-stationary distributions and the continuous-state branching process conditioned to be never extinct

  title={Quasi-stationary distributions and the continuous-state branching process conditioned to be never extinct},
  author={Amaury Lambert},
We consider continuous-state branching (CB) processes which become extinct (i.e., hit 0) with positive probability. We characterize all the quasi-stationary distributions (QSD) for the CB-process as a stochastically monotone family indexed by a real number. We prove that the minimal element of this family is the so-called Yaglom quasi-stationary distribution, that is, the limit of one-dimensional marginals conditioned on being nonzero. Next, we consider the branching process conditioned on not… CONTINUE READING
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