Probably better to eat after. Have a big glass o' water before you jog, then jog, then eat. Otherwise your blood is all in your stomach working on  digesting breakfast instead of out in your limbs carrying oxygen. Also, supposedly there is a "protein window" of about an hour after exercise when your body is much more able to utilize dietary protein.

Exception: If you wait an hour between breakfast and jogging then you can use all that extra chow as fuel. A relatively light, good-carbohydrate breakfast (like oatmeal with some fresh or dried fruit) is best for this, rather than, say, ham and eggs.

I'm not a nutritionist or anything, just someone who used to work out more than I do now. I'd normally work out between 1-4 hours after eating and eat something high-protein just after getting home from the gym, with good results. Work out too soon after eating and I'd have a rotten time and a tummy ache.

If you can go to sleep right after a workout, go for it.