STIT tessellations are Bernoulli and standard

Abstract

Let (Yt : t > 0) be a STIT tessellation process and a > 1. We prove that the random sequence (anYan : n [épsilon] Z) is a non-anticipating factor of a Bernoulli shift. We deduce that the continuous time process (atYat : t [épsilon] R) is a Bernoulli flow. We use the techniques and results in Martínez and Nagel [Ergodic description of STIT tessellations. Stochastics 84(1) (2012), 113–134]. We also show that the filtration associated to the nonanticipating factor is standard in Vershik’s sense.