This one is a difficult one in schizophrenia for me. For my intrusive thoughts and hallucinations typically have such outrageous contents that I do not want to own them. They seem to go against the things I used to be most sure about myself. This gives rise to a tension for me. Because of these contents, it is difficult to accept it is me generating these thoughts.
On top of that, their mode of presentation is diffferent from my usual thoughts that I can or cannot own at will. Hallucinations present themselves as alien, as not-mine. In their form, and sometimes also their content. Similarly, intrusive thoughts feel different in mode of presentation than regular cogitations. Beyond control - the very lack of a sense of ownership is what makes these thoughts appear intrusive to begin with.
Now, I do believe in, and have experience with, the transformation of such symptoms through reconceptualization. That is to say, to conceptualize a hallucination as a hallucination, rather than as a distinct alien subject - this makes a difference for my (emotional) reactions to it. In similar fashion, if I would be able to claim ownership over intrusive thoughts, almost per definition, I would not be surprised if their mode of presentation would alter as well. Yet their outrageous contents stand in the way of doing so for me. So I do not quite own them but conceive of them as products of an illness that is not-me.
One approach that I have used to move towards ownership over such thoughts, granted, a very small step, is the following. Whenever the contents are negative, I conceive of it as an expression of my discomfort, and as such I can own them. Whenever they are positive, I can own them as expression of a good mood.