Markov branching processes with disasters: Extinction, survival and duality to p-jump processes

@article{Hermann2018MarkovBP,
  title={Markov branching processes with disasters: Extinction, survival and duality to p-jump processes},
  author={Felix Hermann and Peter Pfaffelhuber},
  journal={arXiv: Probability},
  year={2018}
}
A $p$-jump process is a piecewise deterministic Markov process with jumps by a factor of $p$. We prove a limit theorem for such processes on the unit interval. Via duality with respect to probability generating functions, we deduce limiting results for the survival probabilities of time-homogeneous branching processes with arbitrary offspring distributions, underlying binomial disasters. Extending this method, we obtain corresponding results for time-inhomogeneous birth-death processes… Expand
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