Accessing ethernet Arduino on LAN from internet?

Can you set your DMZ on your router to the private ip of the Arduino? That will perform a destination nat from your public ip to the Arduino private ip.

Or you can assign a public ip to the Arduino.

edit: Whoa! Is that a Karma value on the user info above the number of posts? That will be handy helping new people determine who can help them. Miktrotik uses that very effectively. I'm SurferTim there also.
http://forum.mikrotik.com/