publication . Preprint . Article . 2010

Unique Bernoulli $g$-measures

Anders Johannson; Anders Öberg; Mark Pollicott;
Open Access English
  • Published: 05 Apr 2010
Abstract
We improve and subsume the conditions of Johansson and \"Oberg [18] and Berbee [2] for uniqueness of a g-measure, i.e., a stationary distribution for chains with complete connections. In addition, we prove that these unique g-measures have Bernoulli natural extensions. In particular, we obtain a unique g-measure that has the Bernoulli property for the full shift on finitely many states under any one of the following additional assumptions. (1) $$\sum_{n=1}^\infty (\var_n \log g)^2<\infty,$$ (2) For any fixed $\epsilon>0$, $$\sum_{n=1}^\infty e^{-(\{1}{2}+\epsilon) (\var_1 \log g+...+\var_n \log g)}=\infty,$$ (3) $$\var_n \log g=\ordo{\{1}{\sqrt{n}}}, \quad n\to ...
Subjects
free text keywords: Mathematics - Dynamical Systems, Mathematics - Probability, Primary 37A05, 37A35, 60G10, Applied Mathematics, General Mathematics, Transfer operator, Uniqueness, Topology, Bernoulli's principle, Mathematical analysis, Iterated function, Wasserstein metric, Bernoulli process, Bernoulli scheme, Mathematics, Stationary distribution
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publication . Preprint . Article . 2010

Unique Bernoulli $g$-measures

Anders Johannson; Anders Öberg; Mark Pollicott;