On Some Impulse Control Problems with Long Run Average Cost

Some particular impulse control problems with infinite horizon and long run average cost are considered for Markov processes having “nice” ergodicity properties.The main feature of the method is to start with discounted cost and then let the discount factor go to zero. This also gives an opportunity to study the asymptotic behavior of some optimal stopping time problems when the discount factor goes to zero. Probabilistic and analytical methods are used and examples are given, especially for Markov jump process and diffusion processes with reflection.