Controlled Multitype Branching Models: Geometric Growth

2000 Mathematics Subject Classi cation: 60J80, 60F25.

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.

This research was supported by the Ministerio de Educacin y Ciencia and the FEDER through the Plan Nacional de Investigaci on Cient ca, Desarrollo e Innovaci on Tecnol ogica, grants BFM2003-06074 and MTM2006-08891.