A note on the Ross\\2-Taylor theorem

Abstract

In this note the condition used in proving a result due to S.M. Ross and H.M. Taylor are examined. These results pertain to the existence of bounded solutions to the average cost optimality equation for controlled Markov processes with an average cost criterion. In particular, we show how the use of commonly found convexity (concavity) properties of value functions can be employed to verify a seemingly rather restrictive equicontinuity condition. In addition, we remark that several results in the literature can be viewed as special cases of the result by Ross and Taylor, contrary to claims otherwise.