Details

Autor(en) / Beteiligte

• Bulatek, W.
• Lemanczyk, M.
• Lesigne, E.

Titel

On the filtering problem for stationary random /spl Zopf//sup 2/-fields

Ist Teil von

• IEEE transactions on information theory, 2005-10, Vol.51 (10), p.3586-3593

Ort / Verlag

IEEE

Erscheinungsjahr

2005

Link zum Volltext

• IEEE_Xplore

Quelle

IEEE Xplore

Beschreibungen/Notizen

• It is shown that whenever a stationary random field (Z/sub n,m/)/sub n,m/spl isin/z/ is given by a Borel function f:/spl Ropf//sup z/ /spl times/ /spl Ropf//sup z/ /spl rarr/ /spl Ropf/ of two stationary processes (X/sub n/)/sub n/spl isin/z/ and (Y/sub m/)/sub m/spl isin/z/ i.e., then (Z/sub n, m/) = (f((X/sub n+k/)/sub k/spl epsi/z/, (Y/sub m + /spl lscr// )/sub /spl lscr/ /spl epsi/z/)) under a mild first coordinate univalence assumption on f, the process (X/sub n/)/sub n/spl isin/z/ is measurable with respect to (Z/sub n,m/)/sub n,m/spl epsi/z/ whenever the process (Y/sub m/)/sub m/spl isin/z/ is ergodic. 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 with the process does not contain a nontrivial compact subgroup.