Alright, here is my undereducated, slightly muddled by need of sleep definition of existence: Because there is no way to know that we actually exist, existence to use would be defined as what we actually know to have a presence in our lives. just because something is an illusion, doesn't mean that it doesn't exist. It isn't alive or even genuine, but it manages to affect us, therefore it does to us, exist. By accepting it's presence in the world, we sort of give it an existence.
You may say, but kitkatkan, if you ignore something, does it exist? That depends on what context of ignore you are talking about. If you know something exists, actually seen it, but you deny it's presence, then you're just being a dick. If you are ignorant of something, then it doesn't exist to you- not yet. Existence
to the universe in general is a different thing, but as far as we can see, only what we know exists. As for the world in general existing, maybe we won't exist to whatever "Existent" world there is. but at least to ourselves, we exist.
actually i think that's just a muddled up version of what holk said, but i'd like to think that that was my own muddled two cents.