On the filtering problem for stationary random Z^2-fields

Wojciech Bulatek (1) , Mariusz Lemanczyk (1) , Emmanuel Lesigne (2)

1 Faculty of Mathematics and Computer Sciences
2 LMPT - Laboratoire de Mathématiques et Physique Théorique

The notion of universal filtering property of an ergodic stationary process is introduced and then using ergodic theory methods it is shown that an ergodic stationary process has this property if and only if the centralizer of the dynamical system canonically associated to the process does not contain a non-trivial compact subgroup.

Mots clés: ergodic theory; filtering; disjointness

Domaines: Systèmes dynamiques [math.DS]

Wojciech Bulatek, Mariusz Lemanczyk, Emmanuel Lesigne. On the filtering problem for stationary random Z^2-fields. IEEE Transactions on Information Theory, 2005, 51, pp.3586-3595. ⟨hal-00016962⟩