On L2-Convergence in a Class of Homogeneous Multitype Markov Chains.

A class of homogeneous multitype Markov chains whose states have non-negative integer coordinates is considered in a situation similar to the supercritical case for branching processes. We establish the geometric growth of the chain, suitably normed, by investigating its almost sure and L2-convergence. Both sufficient and necessary conditions for these convergences are provided depending on certain constraints on the transition mean vectors and the transition covariance matrices of the chain. Finally, we apply the obtained results to a general class of controlled multitype branching processes. [ABSTRACT FROM AUTHOR]