I don't claim to understand how these capacitve pens work exactly but since the screen is detecting minute electrical charges I would guess that there is an excess of charge at play. This will sound wierd, but try putting the phone down and use the stylus while wearing gloves (or if you have one of the antistatic bags electronic components get delivered in that would be the best). If the pen behaves normally then, to be blunt, you are the problem

since you seem to be charged statically, and need to ground yourself or change to all cotton clothing. Otherwise you have a defective pen and should get it changed.
Hope this helps (and was not too rude)!
Regards,
Eric.