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We consider a class of stochastic control problems where uncertainty is due to driving noises of general nature as well as to rapidly fluctuating processes affecting the drift. We show that, when the noise "intensity" is small and the fluctuations become fast, the stochastic problems can be approximated by a deterministic one. We also show that the optimal control of the deterministic problem is asymptotically optimal for the stochastic problems.doi:10.1137/s0363012993254540 fatcat:juuu53t4q5gxzadd7rfjbtthta