Ergodic Description of STIT Tessellations

Let (Y_t: t > 0) be the STIT tessellation process. We show that for all polytopes W with nonempty interior and all a>1, the renormalized random sequence (a^n Y_{a^n}: n integer) induced in W, is a finitary factor of a Bernoulli shift. As a corollary we get that the renormalized continuous time process (a^t Y_{a^t}: t real) induced in W is a Bernoulli flow.