Controlled Martingale Problems And Their Markov Mimics

09/01/2023

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by   Siva Athreya, et al.

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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.