Nonnegative matrices, generalized eigenvectors and dynamic programming

In this paper we present a detailed analysis of the structure of a set of nonnegative matrices (not necessarily stochastic) which plays a role in several dynamic programming recursions (Makov decision processes, Leontief substitution systems). We investigate the asymptotic behaviour of these recursions and give an application, arising from the study of sensitive optimality criteria in Markov decision processes.