A note on some new results on the ergodic control of partially observed Markov chains

In an early paper (Chuang, D. M. and Arapostathis, A., 1999), the ergodic control problem of partially observed Markov chains was studied. A major assumption was proposed to justify the existence of the optimal policy characterized by a dynamic programming equation. In this note we show that the major assumption, though quite general and easily verifiable, is not satisfied by an important class of machine maintenance problems. A modified version of the assumption is thus presented to improve this shortage and an example is analyzed to show our work.