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A Limit Theorem for Multi-Type Subcritical Age-Dependent Branching Processes with two Types of Immigration
Mathematics and Education in Mathematics, Tome 40 (2011) no. 1, pp. 314-319 Cet article a éte moissonné depuis la source Bulgarian Digital Mathematics Library

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This work continues the study of the classical subcritical age-dependent branching process and the effect of the following two-type immigration pattern in multidimensional case. At a sequence of renewal epochs a random number of immigrants of different types enters the population. Each subpopulation stemming from one of these immigrants is revived by new immigrants and their offspring whenever it dies out, possibly after an additional delay period. Individuals from the same type have the same lifetime distribution and produce offspring according to the same reproduction law. This is the p-dimensional Bellman-Harris process with immigration at zero and immigration of renewal type (BHPIOR). With this paper we complete the study of the one-dimensional case with its multi-type counterpart generalizing the convergence in probability for such processes. *2000 Mathematics Subject Classification: 60J80, 60K10.
Keywords: Multi-Dimensional Bellman-Harris Process, Galton-Watson Process, Immigration at Zero, Immigration of Renewal Type, Regenerative Process 
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Slavtchova-Bojkova, Maroussia. A Limit Theorem for Multi-Type Subcritical Age-Dependent Branching Processes with two Types of Immigration. Mathematics and Education in Mathematics, Tome 40 (2011) no. 1, pp. 314-319. http://geodesic.mathdoc.fr/item/MEM_2011_40_1_a36/