Look in "Options->Controls->Map Controllers". Watch the numbers in parantheses next to each axis. If they are arbitrarily changing while you are not touching the stick, then select the axis, check the "Advanced" option, and up the deadband a little.
Now, put your hand on the stick and hold it as steady as you can. Watch the numbers again and repeat until the errant inputs are ignored. A little damping might also cure the issue. Damping just slows the reaction to stick deflections a little.
In either case, a little goes a long way. In the Advanced panel are two graphs. One shows the raw input from the stick. The other shows the input after you make adjustments.