A Limit Theorem for Multi-Type Subcritical Age-Dependent Branching Processes with two Types of Immigration

Марусия Н. Славчова-Божкова - В настоящата работа се обобщава една гранична теорема за докритичен многомерен разклоняващ се процес, зависещ от възрастта на частиците с два типа имиграция. Целта е да се обобщи аналогичен резултат в едномерния случай като се прилагат “coupling” метода, теория на възстановяването и регенериращи процеси.

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.

The research was partially supported by appropriated state funds for research allocated to Sofia University (contract No 112/2010), Bulgaria.