Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Pliska Studia Mathematica Bulgarica, Vol. 18, No 1, (2007), 103p-110p
In this work we deal with a multitype branching process that puts together control in the number of reproductive units of each type and population size - dependent reproduction. Moreover, unlike other branching models, it is possible interaction between individuals at reproduction time. We investigate sufficient conditions for such a model to have asymptotically a geometric growth, considering almost sure and Lα, 1 ≤ α ≤ 2, convergences. We pay special attention to L2 convergence, taking advantage of the Hilbertian properties of this space.