On an approximation of average cost per unit time impulse control of Markov processes

TL;DR

This paper studies impulse control of continuous-time Markov processes with average cost criteria, proposing an approximation method via exit-time stopping problems and solving the Bellman equation to find near-optimal solutions.

Contribution

It introduces an approximation approach for impulse control problems using exit-time stopping problems and provides solutions to the Bellman equation for the original problem.

Findings

Stopped impulse control problems approximate the optimal value.

Solution to the Bellman equation characterizes the optimal control.

The method offers a practical way to solve complex impulse control problems.

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 increasing sequence of open sets. We find solution to Bellman equation corresponding to the original problem and show that stopped impulse control problems approximate optimal value of the cost functional.