CHAPMAN-KOLMOGOROV EQUATION FOR NON-MARKOVIAN SHIFT-INVARIANT MEASURES

• 成果类型: Article
• 署名作者: COURBAGE, M; HAMDAN, D
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176988618
• 发表日期: 1994
• 页码: 1662-1677
• 关键词: dynamical-systems

摘要

We study the class C-pi of probability measures invariant with respect to the shift transformation on K-Z (where K is a finite set of integers) which satisfies the Chapman-Kolmogorov equation for a given stochastic matrix Pi. We construct a dense subset of measures in C-pi distinct from the Markov measure. When Pi is irreducible and aperiodic, these measures are ergodic but not weakly mixing. We show that the set of measures with infinite memory is G(delta) dense in C-pi and that the Markov measure is the unique measure which maximizes the Kolmogorov-Sinai (K-S) entropy in C pi. We give examples of ergodic measures in C-pi with zero entropy.