Optimal Control of Markov Chains Admitting Strong and Weak Interactions

The singular perturbation problem is shown to decompose into two optimization problems. The first of these optimization problems, the “limit problem”, captures the effect of show process in the orignal system. The solution to this limit problem approximates the value function for the original problem by O(E). The rest of the decomposition is the so-called “fast problem”, which captures effects of processes that change quickly with respect to those in the limit problem.