Which is also what happens with beliefs. Depending on the study, there is something like a 20-90ms lapse between the unconscious - where thoughts and beliefs come from - and us being conscious of them. However, sometimes we may never become conscious of them. It's in that gap where we perceive that the thought or belief is 'ours'. As to whether or not the thoughts are ours or not depend on your model of the self. Spiritually-speaking thoughts and beliefs are not 'us' but are karas or 'invented things' - roughly the 'things' of perceptual/created reality.