Determination of the spectral radius of a Markov decision process

Consider a Markov decision process in the situation of discrete time, finite state space and finite action space. A positive probability for fading of the system is allowed. In this case, contraction properties of certain operators, used in Dynamic Programming, are strictly related to the spectral radius of the process. In this paper a method for estimating this spectral radius is proposed. The result can be extended immediately to the case in which the transition probability matrices are replaced by general nonnegative matrices.