How does the RQ4-Global Hawk improve stability? I have seen several videos recorded from an UAV in which the stabilization of the camera is almost perfect. Cameras are installed in a gimbal, of course, but do new drones introduce some new technology in order to improve the stability? 

We can take, for example, the RQ-4 Global Hawk (first flight in 1998) and the Chendgu HQ (First flight in 2012). Note that the HQ-4 Xianglong's airframe topology its quite similar to the RQ-Global Haw, however it has a special wing configuration.
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".