A Note on the Extinction Problem for Controlled Multitype Branching Processes

2000 Mathematics Subject Classification: 60J80, 60J10.In this paper we consider a discrete time controlled multitype branching process with random control in discrete time. We provide sufficient conditions for the almost sure extinction of the process as well as for its indefinite growth with a positive probability. Moreover an illustrative example is shown and some simulations are given.Research supported by the Ministerio de Ciencia y Tecnologia and the FEDER through the Plan Nacional de Investigaci on Cientifica, Desarrollo e Innovacion Tecnologica, grant BFM2003-06074