Well this is the most common dream and you have found the most common solution.

Its when people have these reccuring dreams specifically about something chasing them.

Eventually the person may experiance "lucid dreaming". it can take the form of actual lucid dream or believeing you are in control inside the dream but your not.

When this happens you have the oppertunity to change it, when you do every dream you have of it after that will be changed (if you dream of it after that at all, which is usually defined by how well you do in that dream at conquering the person following you).

Eventually the importance of the dream diminishes and then ceases to exist and im not sure why the importance of the dream diminishes (your confidence in this case?)

Its very common.