Stability and singular perturbations in constrained Markov decisionproblems

Constrained Markov decision problems (CMDPs) with the average cost criterion and a single ergodic chain, or the discounted cost with a general multichain structure, are considered. Conditions for stability of the optimal value and control to changes of the parameters of the problem, such as immediate costs, transition probabilities, and the discount factor, are established. Singular constrained problems, for which the optimal value and controls exhibit discontinuities, are studied