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Stochastic Models, 21(1):133147, 2005 Copyright Taylor & Francis, Inc.
 

Summary: Stochastic Models, 21(1):133­147, 2005
Copyright © Taylor & Francis, Inc.
ISSN: 1532-6349 print/1532-4214 online
DOI: 10.1081/STM-200046495
LIMIT THEOREMS FOR SUBCRITICAL AGE-DEPENDENT BRANCHING
PROCESSES WITH TWO TYPES OF IMMIGRATION
Gerold Alsmeyer Institut für Mathematische Statistik Fachbereich Mathematik,
Westfälische Wilhelms-Universität Münster, Münster, Germany
Maroussia Slavtchova-Bojkova Department of Probability and Statistics,
Institute of Mathematics and Informatics, Bulgarian Academy of Sciences,
Sofia, Bulgaria
For the classical subcritical age-dependent branching process the effect of the following
two-type immigration pattern is studied. At a sequence of renewal epochs a random number of
immigrants enters the population. Each subpopulation stemming from one of these immigrants
or one of the ancestors is revived by new immigrants and their offspring whenever it dies out,
possibly after an additional delay period. All individuals have the same lifetime distribution and
produce offspring according to the same reproduction law. This is the Bellman-Harris process
with immigration at zero and immigration of renewal type (BHPIOR). We prove a strong
law of large numbers and a central limit theorem for such processes. Similar conclusions are
obtained for their discrete-time counterparts (lifetime per individual equals one), called Galton-

  

Source: Alsmeyer, Gerold - Institut für Mathematische Statistik, Westfälische Wilhelms-Universität Münster

 

Collections: Mathematics