Branching Brownian motion in strip: survival near criticality

@article{Harris2012BranchingBM,
  title={Branching Brownian motion in strip: survival near criticality},
  author={Simon Harris and Marion Hesse and Andreas E. Kyprianou},
  journal={arXiv: Probability},
  year={2012}
}
We consider a branching Brownian motion with linear drift in which particles are killed on exiting the interval (0,K) and study the evolution of the process on the event of survival as the width of the interval shrinks to the critical value at which survival is no longer possible. We combine spine techniques and a backbone decomposition to obtain exact asymptotics for the near-critical survival probability. This allows us to deduce the existence of a quasi-stationary limit result for the… 

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