On impulsive control with long run average cost criterion
The impulsive control with long run average cost criterion was considered first by M. Robin in [2], for Markov processes having nice ergodic properties. The aim of this paper is to complete and extend the results of paper [2]. In particular we show that for Fellerien Markov processes the optimal value is constant and find optimal or ɛ-optimal strategies. We also prove, that the use of general stopping times, instead of those of the form τi = τi−1 + σi ° \(\tau _i = \tau _{i - 1} + \sigma _i \circ \theta \tau _{\tau _{_{i - 1} } }\) as in the paper [2] does not change the optimal value of the functional. Results are only reported here and the detailed proofs will appear elsewhere, see [3].