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A Markov policy γ∈ΓM\gamma\in\Gamma_{M}γ∈ΓM applied to a Controlled Markov Chain induces a process {Xt,t≥0}\{ X_{t},t\ge0 \}{Xt,t≥0} which is Markov.
If the policy γ∈ΓS\gamma\in\Gamma_{S}γ∈ΓS then (Xt)t≥0(X_{t})_{t\ge0}(Xt)t≥0 is stationary.