Target-level criterion in Markov decision-processes

The Markov decision process is studied under the maximization of the probability that total discounted rewards exceed a target level. The authors focus on and study the dynamic programming equations of the model. They give various properties of the optimal return operator and, for the infinite planning-horizon model, the authors characterize the optimal value function as a maximal fixed point of the previous operator. Various turnpike results relating the finite and infinite-horizon models are also given.