I am searching for a good illustration of the concept of a filtration. So far this https://books.google.de/books?id=OBOGDwAAQBAJ&pg=PA218#v=onepage&q&f=false book had a nice illustration showcasing a tree diagram for a coin toss experiment, where each coin toss can be up or down.
I am still not completely sure how to interpret it. Is the n-th filtration the union of the sets in the n-th level of the tree?
Maybe someone could explain it to me or make an even nicer illustration showing the sets of possible realizations (in each tree node) and how I then construct the n-th filtration from this.
I am also open to an even better illustration (without a tree) which would help my understanding.
Maybe you can also find some words about why filtrations are useful. Currently, my understanding is, that filtrations are especially useful for describing the sample space $\Omega$ of stochastic experiments which are sequential in nature.