You can allow students to edit and delete their own discussion posts by changing the settings from the Discussions page.
This setting can also be changed from the Course Settings page.
Note: When enabled, this setting also applies to group discussions.
Edit Discussion Settings
Check the Edit and delete their own posts checkbox.
Note: Unchecking this option will restrict students from editing and deleting their own Discussion posts. This permission affects posts in new discussion topics, discussion replies, and discussions within course groups.