Existence of Optimal Markov Solutions for Ergodic Control of Markov Processes

摘要

For the ergodic control problem for a large class of controlled Markov processes in continuous time, existence of an optimal ergodic solution and an optimal, possibly time-inhomogeneous Markov solution, in both cases corresponding to a stationary Markov relaxed control policy, are known separately under suitable conditions (Bhatt and Borkar, 1996). The aim of this article is to refine this result to establish the existence of an optimal time-homogeneous Markov solution. The proof is based upon Krylov's Markov selection procedure.