A Pseudo-Markov Property for Controlled Diffusion Processes

Abstract : In this note, we propose two different approaches to rigorously justify a pseudo-Markov property for controlled diffusion processes which is often (explicitly or implicitly) used to prove the dynamic programming principle in the stochastic control literature. The first approach develops a sketch of proof proposed by Fleming and Souganidis [9]. The second approach is based on an enlargement of the original state space and a controlled martingale problem. We clarify some measurability and topological issues raised by these two approaches.
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Julien Claisse, Denis Talay, Xiaolu Tan. A Pseudo-Markov Property for Controlled Diffusion Processes. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2016, 54 (2), pp.1017 - 1029. ⟨10.1137/151004252⟩. ⟨hal-01429545⟩

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