When in transit at Ataturk international airport, you do not pass through passport controls. Therefore, you would not need a transit visa.
However, if you have to pick up your bags and re-check your bags, or if you have to move from Ataturk to Sahiba Gokcen (or vice versa), you will go through passport control and will need a transit visa.
I don’t see how being stateless affects any of this, but I might be missing something.
Credit:stackoverflow.com‘