How does the RQ4-Global Hawk improve stability?
What you are looking for is "gyroscopic-stabilization".

As you can see in this video, the camera is mounted on gimbals that can rotate over all axis. Movements are controlled thanks to gyroscopes. For sensors mounted on larger aircraft, optronics systems are ball-shapes. That way they can rotate without modifying aerodynamics. There is no need to compensate for translation as targets are far away. 

I didn't find any sources for shake reduction thus I can only assume techniques are the one that Wikipedia name "vibration reduction" and "anti-shake".