Rates of Growth in a Class of Homogeneous Multidimensional Markov Chains

M. González, R. Martínez, M. Mota
2006 Journal of Applied Probability  
We investigate the asymptotic behaviour of homogeneous multidimensional Markov chains whose states have nonnegative integer components. We obtain growth rates for these models in a situation similar to the near-critical case for branching processes, provided that they converge to infinity with positive probability. Finally, the general theoretical results are applied to a class of controlled multitype branching process in which random control is allowed.
doi:10.1239/jap/1143936250 fatcat:rwzfau2yo5a7zpvljd7wlqpsva