6533b7d1fe1ef96bd125d5a5

RESEARCH PRODUCT

The Extinction of Generations in Generation-Dependent Bellman-Harris Branching Processes with Exponential Lifespan

Lutz Edler

subject

Branching (linguistics)education.field_of_studyDistribution (mathematics)ExtinctionExponential distributionMarkov chainPopulationQuantitative Biology::Populations and EvolutionStatistical physicseducationExponential functionMathematicsPoisson limit theorem

description

If V 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 , P(V > 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.

yearjournalcountryeditionlanguage
1978-01-01
https://doi.org/10.1007/978-94-009-9857-5_17