If we have a Markov Ito process (where the coefficients of dt and dW(t) don't depend on past values of the process), then looking at the past values won't give any extra knowledge about likely future movements of the process. Weak-form EMH says all past prices are already incorporated in the current price, so again, looking at the past won't help you. So this is consistent with the above. However, if we make the coefficients of the Ito process depend on past values, then we'd have a process that goes against weak-form EMH.
