Quelques remarques sur les facteurs des systèmes dynamiques gaussiens

• Autorzy: Anzelm Iwanik , Mariusz Lemańczyk , T. de la Rue , J. de Sam Lazaro
• Języki publikacji: FR EN

Abstrakty

EN

We study the factors of Gaussian dynamical systems which are generated by functions depending only on a finite number of coordinates. As an application, we show that for Gaussian automorphisms with simple spectrum, the partition ${(X_0 ≤ 0), (X_0 > 0)}$ is generating.

Kategorie tematyczne

• 60G15: Gaussian processes
• 28D05: Measure-preserving transformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1997
• Tom: 125
• Numer: 3
• Strony: 247-254

Daty

wydano

1997

otrzymano

1996-06-12

poprawiono

1996-07-01

Twórcy

autor

Anzelm Iwanik

• Institute of Mathematics, Technical University of Wrocław, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Pologne

autor

Mariusz Lemańczyk

• Department of Mathematics and Computer Science, Nicolas Copernicus University, Chopina 12/18, 87-100 Toruń, Pologne

autor

T. de la Rue

• Analyse et Modèles Stochastiques, URA CNRS 1378, Université de Rouen, 76821 Mont-Saint-Aignan Cedex, France

autor

J. de Sam Lazaro

• Analyse et Modèles Stochastiques, URA CNRS 1378, Université de Rouen, 76821 Mont-Saint-Aignan Cedex, France

Bibliografia

• [1] I. P. Cornfeld, S. V. Fomin and Y. G. Sinai, Ergodic Theory, Springer, 1982.
• [2] M. Lemańczyk, F. Parreau and J.-P. Thouvenot, On the disjointness problem for Gaussian automorphisms, preprint.
• [3] M. Lemańczyk and F. Parreau, Gaussian automorphisms whose self-joinings are Gaussian, preprint.
• [4] M. Lemańczyk and J. de Sam Lazaro, Spectral analysis of certain compact factors for Gaussian dynamical systems, Israel J. Math. (1996), à paraître.
• [5] L. H. Loomis, An Introduction to Abstract Harmonic Analysis, Van Nostrand, Princeton, 1953.
• [6] D. Newton, On Gaussian processes with simple spectrum, Z. Wahrsch. Verw. Gebiete 5 (1966), 207-209.
• [7] D. Newton and W. Parry, On a factor automorphism of a normal dynamical system, Ann. Math. Statist. 37 (1966), 1528-1533.
• [8] W. Parry, Generators in Ergodic Theory, Benjamin, New York, 1969.
• [9] T. de la Rue, Entropie d'un système dynamique gaussien : cas d'une action de $ℤ^d$, C. R. Acad. Sci. Paris Sér. I 317 (1993), 191-194.
• [10] J. P. Thouvenot, Some properties and applications of joinings in ergodic theory, in: Ergodic Theory and its Connections with Harmonic Analysis, London Math. Soc. Lecture Note Ser. 205, Cambridge Univ. Press, 1995, 207-235.
• [11] J. P. Thouvenot, Utilisation des processus gaussiens en théorie ergodique, preprint.