Velocity vs Position response

[Bobkingmen3]

Currently the position of the controller stick maps to the velocity that the mouse is moved at.
Is there a option or a slight code change that could be made to enable the controller stick position to map to the mouse position.

Basically what I am asking for is that when I push my stick to the right the cursor goes to the right side of the screen then when I release it snaps back to center of the screen. Currently if I push the stick right the cursor begins moving right, then when I let go of stick the cursor stops moving.

Is this at least simple to change with some sort of mapping function, pls let me know.