On ergodic stopping and impulsive control problems for nonuniformly ergodic Markov processes

In this paper we study optimal stopping and impulse control with a long-run average cost functional for ergodic Markov processes, which transition semigroupP _t converges uniformly on compact sets to a unique invariant measure, ast. We restrict the class of strategies to so-called stopping rules and obtain continuity of value functions and characterization of optimal rules.