On Strong 1-optimal Policies in Markov Control Processes with Borel State Spaces

摘要

We consider Markov control processes (MCPs) with a Borel state space satisfying certain stochastic stability assumptions on the transition structure which imply the so-called V-uniform geometric ergodicity of Markov chains induced by stationary policies. Using standard regularity conditions and assuming that the transition probability has a density function, we provide a new existence theorem for strong 1-optimal policies in MCPs with unbounded costs.