Basis for belief that a person can be "possessed by" a demon?

I'm asking a rather technical question here. I'm wondering where the idea comes from that a person could be "**possessed by**" a demon; as in, the demon "possesses" / "owns" the person -- as opposed to the person simply "having" / "possess**ing**" a demon which does things through and for the person. I understand that there are examples in Scripture where demons give people supernatural abilities like special knowledge or unnatural strength. I also understand that there are examples in Scripture of demons doing things to people like speaking through them or throwing them around. However, my car does things to me that I don't want it to sometimes, but it doesn't "possess" me / "own" me. I own my car. It just doesn't always do what I want it to -- it could even cause me harm (if the brakes went out or something) -- but that has more to do with it not doing what I want it to than it "owning" me. Hopefully this distinction is making sense. The reason I ask is that I looked up the Greek behind a couple of the instances of "demon possession" in Scripture (Luke 4:33; 8:27) and in both places it is **translated** to say that the person was possessed by a demon, but in both cases the **Greek** suggests that the *person* possessed the *demon*. **Is there anything explicit in Scripture which describes a person being "possessed by" a demon? If not, what is the origin of this belief?**