We consider Markov control processes with Borel state space and Feller transition probabilities, satisfying some generalized geometric ergodicity conditions. We provide a new theorem on the existence of a solution to the average cost optimality equation.  2005 Elsevier Inc. All rights reserved.

This paper deals with discrete-time Markov control processes on a general state space. A long-run risk-sensitive average cost criterion is used as a performance measure. The one-step cost function is nonnegative and possibly unbounded. Using the vanishing discount factor approach, the optimality inequality and an optimal stationary strategy for the decision maker are established.Comment: Published at http://dx.doi.org/10.1214/105051606000000790 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

We study an altruistic growth model with production uncertainty viewed as an intergenerational stochastic game. The existence of stationary Markov perfect equilibria is proved under general assumptions on utility functions for the generations and for non-atomic transition probabilities. This paper answers some issues that arose from the literature in the 1980s decade.