Before revision: We prove continuity of a controlled SDE solution in Skorokhod's J_1 and M _1 topologies and also uniformly, in probability, as a non-linear functional of the control strategy.
After revision: We prove continuity of a controlled SDE solution in Skorokhod's M_1 and J _1 topologies and also uniformly, in probability, as a non-linear functional of the control strategy.