Abstract
Markov branching processes and in particular birth-and-death processes are considered under the influence of disasters that arrive independently of the present population size. For these processes we derive an integral equation involving a shifted and rescaled argument. The main emphasis, however, is on the (random) probability of extinction. Its distribution density satisfies an equation which can be solved numerically at least up to a multiplicative constant. In an example it is also found by simulation.
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Bartoszynski, R., Bühler, W.J., Chan, W. et al. Population processes under the influence of disasters occurring independently of population size. J. Math. Biology 27, 167–178 (1989). https://doi.org/10.1007/BF00276101
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DOI: https://doi.org/10.1007/BF00276101