In this article we prove under suitable assumptions that the marginals of any solution to a relaxed controlled martingale problem on a Polish space $E$ can be mimicked by a Markovian solution of a Markov-relaxed controlled martingale problem. We also show how such `Markov mimics' can be obtained by relative entropy minimisation. We provide many examples where the above results can be applied.

翻译：本文在适当假设下证明，波兰空间$E$上任意松弛受控鞅问题的解的边际分布，可由某个马尔可夫松弛受控鞅问题的马尔可夫解模拟。我们还展示了如何通过相对熵最小化获得此类"马尔可夫模拟"，并提供了大量可应用上述结果的实例。