On ergodic stopping and impulsive control problem for nonuniformly ergodic Markov processes (Q1111238)

Optimal stopping and impulse control problems with a long run average cost functional for ergodic Markov processes are considered. It is assumed that the transition semigroup converges uniformly on compact sets to a unique invariant measure, as time tends to infinity. This ergodicity assumption is weaker than the one usually made, but instead, other rather restrictive and complicated assumptions on the process and on the admissible stopping rules are imposed. It is proven that the value function is continuous and the optimal rules are characterized.