Abstract
If V<k> is the time when in a Bellman-Harris branching model the k-th generation disappears out of the population, and if all individuals have exponentially distributed lifespans, the asymptotic behavior of the tail of the distribution of the extinction time V<k>, P(V<k> > t), is obtained, even if the distributions of the lifespans and the offspring sizes vary generation-dependent. Furthermore the times of extinction of several successive generations can be specified for the generation- independent case of the Markov branching model in continuous time. If the initial number of individuals and the absolute time grow up appropriately linked, a Poisson limit theorem for generation sizes will be given.
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© 1978 ACADEMIA, Publishing House of the Czechoslovak Academy of Sciences, Prague
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Edler, L. (1978). The Extinction of Generations in Generation-Dependent Bellman-Harris Branching Processes with Exponential Lifespan. In: Transactions of the Eighth Prague Conference. Czechoslovak Academy of Sciences, vol 8A. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9857-5_17
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DOI: https://doi.org/10.1007/978-94-009-9857-5_17
Publisher Name: Springer, Dordrecht
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