Persistent download icon in Prestigio (4040 DUO multiphone) pull down menu - even with download over days ago. How to remove it?
If you have android version 4.1 (jelly bean) or later, you can long-press on the notification and view the app settings page of the app that is showing the notification. 

From there, you can force quit the app, or you can permanently disable notifications from that app. 

At the very least, you'll know which app is causing the problem, and you may be able to change something within the app itself.