On an Approximation of Average Cost per Unit Time Impulse Control of Markov Processes

Abstract

In this paper we consider impulse control of continuous time Markov processes with average cost per unit time functional. This problem is approximated using impulse control problems stopped at the first exit time from an increasing sequence of open sets. We find a solution to the Bellman equation corresponding to the original problem and show that stopped impulse control problems approximate optimal value of the cost functional.