Tail fields generated by symbol counts in measure-preserving systems

• Autorzy: Karl Petersen , Jean-Paul Thouvenot
• Języki publikacji: EN

Abstrakty

EN

A finite-state stationary process is called (one- or two-sided) super-K if its (one- or two-sided) super-tail field-generated by keeping track of (initial or central) symbol counts as well as of arbitrarily remote names-is trivial. We prove that for every process (α,T) which has a direct Bernoulli factor there is a generating partition β whose one-sided super-tail equals the usual one-sided tail of β. Consequently, every K-process with a direct Bernoulli factor has a one-sided super-K generator. (This partially answers a question of Petersen and Schmidt.)

Kategorie tematyczne

• 37A50: Relations with probability theory and stochastic processes
• 37A05: Measure-preserving transformations
• 37A35: Entropy and other invariants, isomorphism, classification

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2004
• Tom: 101
• Numer: 1
• Strony: 9-23

Daty

wydano

2004

Twórcy

autor

Karl Petersen

• Department of Mathematics, University of North Carolina, CB 3250, Phillips Hall, Chapel Hill, NC 27599 U.S.A.

autor

Jean-Paul Thouvenot

• Laboratoire de Probabilités, Université Pierre et Marie Curie, 4 place Jussieu, 75252 Paris, France

Identyfikatory

DOI

10.4064/cm101-1-2