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STIT tessellations are Bernoulli and standard

Published online by Cambridge University Press:  29 November 2012

SERVET MARTÍNEZ
SERVET MARTÍNEZ*
Affiliation:
Departamento Ingeniería Matemática and Centro Modelamiento Matemático, Universidad de Chile, UMI 2807 CNRS, Casilla 170-3, Correo 3, Santiago, Chile (email: smartine@dim.uchile.cl)
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Abstract

Let (Yt:t>0) be a STIT tessellation process and a>1. We prove that the random sequence (anYan:n∈ℤ) is a non-anticipating factor of a Bernoulli shift. We deduce that the continuous time process (atYat:t∈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 non-anticipating factor is standard in Vershik’s sense.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 34 , Issue 3 , June 2014 , pp. 876 - 892
Copyright
©2012 Cambridge University Press 

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