Controlled Markov processes on the infinite planning horizon: weighted and overtaking cost criteria

Stochastic control problems for controlled Markov processes models with an infinite planning horizon are considered, under some non-standard cost criteria. The classical discounted and average cost criteria can be viewed as complementary, in the sense that the former captures the short-time and the latter the long-time performance of the system. Thus, the authors study a cost criterion obtained as weighted combinations of these criteria, extending to a general state and control space framework several results by Feinberg and Shwartz (1992), and by Krass et al. (1992). In addition, a functional characterization is given for overtaking optimal policies, for problems with countable state spaces and compact control spaces; the authors´ approach is based on qualitative properties of the optimality equation for problems with an average cost criterion