My understanding is that Hawking radiation is where:

1. a particle/anti-particle pair is created at the event horizon;

2. the particle is on the outside edge of the event horizon, so "escapes" the black hole;

3. the anti-particle is on the inside edge of the horizon, so decreases the size of the black hole due to particle/anti-particle annihilation (with a corresponding particle on the inside of the black hole).