Multi-Dimensional Bellman-Harris Process Galton-Watson Process Immigration at Zero Immigration of Renewal Type Regenerative Process
Issue Date:
2011
Publisher:
Union of Bulgarian Mathematicians
Citation:
Union of Bulgarian Mathematicians, Vol. 40, No 1, (2011), 314p-319p
Abstract:
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.
Description:
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.
