You have changed? In what way?
Most guys say they have changed but when they are put back in the old confronting or challenging situations, they actually respond in exactly the same way as they did before.
When you say "I have changed", she thinks in terms of:
"These are just empty words. I still don't trust it and I don't want to be hurt again..."
If you want to convince her, you will have to explain to her in detail why you have changed and what is different now.
Tell her exactly what you did wrong in the past, recalling a negative experience and tell her exactly how you would respond in the future if this situation happened again.
Telling her that you changed is too vague.
You need to be much more specific and prove to her by action that these changes are real, not just words.
You can start here if you want to:
What exactly did you change?
What exactly would you do differently if you were in a new relationship?
What exactly was the cause of your tensions or break up and how would you deal with these situations today?
To your power!