DOTs stop doing damage when enemy out of range

If you hit an enemy with a spell that has DOT, ie: fire arrow - the DOT will stop doing damage if you get too far away from the enemy, ie:

Echondas attacks Elf Fighter and hits, dealing 16 points of critical damage from Fire Arrow.
Echondas attacks Elf Fighter and hits, dealing 2 points of damage from Fire Arrow.
Echondas attacks Elf Fighter and is out of reach, dealing no damage from Fire Arrow.
Echondas attacks Elf Fighter and is out of reach, dealing no damage from Fire Arrow.
Echondas attacks Elf Fighter and is out of reach, dealing no damage from Fire Arrow.