Question To Quants: Brownian Motion The Drift Parameter Does It Represent Systematic Risk?

I am a relative newbie to stochastic processes, so please bear with me. If we look at standard Brownian motion model:

dS = μdt + σdX

Would I be remotely correct to state that the drift parameter above (μdt) is what can represent systemic component of return that can be described by any of the pricing models out there that relate systematic risk to fair return (CAPM, APT etc) and the last component representing non-systematic risk that is stochastic?

I do realize that the last last component affects the walk path of the price but the central deterministic tendency is still "dominated" by the drift component.or am I completely off here?

I will be grateful for any feedback you guys could offer.

 

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