Although the Xperia Z3 camera lacks the Optical Image Stabilizer (OIS) feature, but thanks to the Intelligent active SteadyShot feature you can record steady videos on Xperia Z3.
To enable the Intelligent active mode while recording video on Xperia Z3, do as follows:
1. Open the Camera application
2. Tap the 3dot icon on the top left to open the Camera Settings.
3. Go to the second tab (with a frame icon)
4. Tap the SteadyShot option and make sure to select the Intelligent active mode
5. Now, get back to the main view of the Camera application and start recording less shaky and blurry videos