Ergodic impulse control with constraint: locally compact case

The impulse control problems for a Markov–Feller process with a long-term cost (ergodic) are considered, but the controls are allowed only when a signal arrives. This is referred to as control problems with constraint. Such problems are studied by the authors in SIAM J. Control. Optim. vol. 54, 55, 56 for the case of a compact metric state space and are extended in [Modeling, Stochastic Control, Optimization, and Applications, Springer, 2019, 427–450] to the situation of a locally compact state space with a uniform ergodicity assumption. The long term average cost problem is re-considered here with a non-uniform ergodicity assumption satisfied, for example, by a large class of diffusion processes in the whole space.