Its a toughie, but here's my analysis:
Believing in yourself or in something you do CAN change the outcome, but only if you withdraw into your beliefs and can ignore the odds/possibilities/etc.
Therefore, I believe that thinking you can change or do something just by believing hard enough is a thought process only the thick headed, extremist type of people can achieve. Ya know, those people you can argue with that the sky is blue, but they think the sky is green and won't even consider it any other way? That's an extreme case, but there are a lot of people like that, negative and positive ones.
If you're a rational-minded person who takes in all the possibilities and examines and observes a situation/event/whatever before coming to a conclusion, it's almost near impossible for belief in something to affect your reality. Simply because you won't be willing to take a risk at very small odds, which is reasonable and logical, so there's nothing wrong with that. Thing is, the people who are famous for starting revolutions, going from nothing to everything, big name artists or writers who lived in poverty; they're more toward the extremist end of the spectrum.
That being said, the answer is it all depends. Who you are, how you grew up, and of course your intelligence quotient. MY answer is yes and no. I believe other people can change their reality, but I don't believe I can change mine simply because I think too much for my own good.