There are a few things to try. Isolating the issue is the most difficult. Go to Options->Controls->Map Controllers.
1) In the "Map Controllers" window, select the stick you are having the issue with.
Now, with your hand off the stick, watch the numbers in the parentheses to see if any are changing on their own. If they are not changing, place your hand on the stick and hold it steady. If the numbers are still not changing, then we need to look else where for that is causing the errant inputs.
If they are changing, for any axis, then we have a potential culprit.
2) Select an axis which has changing numbers. Check the "Advanced" box.
Check the "Enable Scaling" option.
A new flap opens up displaying that axis and a lot of adjustments available.
Ignore the scaling sliders (those 10 vertical sliders), for the moment. Those sliders are best used once you have the errant input under control.
There are two sliders (Damping and Deadband) we are going to start with.
There is also a graph next to those sliders which show the "Raw" versus the "Scaled" input.
If the "Scaled" input is wiggling, then you need to make some adjustments.
Damping impacts the stick motion through the entire range of motion. Deadband impacts the off center motion of the stick. Neither of these options will prevent the full range the stick has available to it. It just alters how the game applies it.
If you can move the stick and the "Scaled" line stays smooth, once you are off center, then you need to apply "Deadband". A little at a time to until the "Scaled" graph stays smooth.
If the "Scaled" graph continues to show errant input after you move and hold the stick in position, then you need to add some "Damping". Again, a little at a time until the "Scaled" graph smooths.
You may need to use both. It just takes a bit of time and patience. Hope that helps.