Analysis of Correlation Bounds for Uniformly Expanding Maps on [0, 1]
In this paper, we provide the decay of correlations for random dynamical systems. Precisely, we consider the uniformly <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="script"&...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-11-01
|
| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/12/12/1072 |
| Summary: | In this paper, we provide the decay of correlations for random dynamical systems. Precisely, we consider the uniformly <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="script">C</mi><mn>2</mn></msup></semantics></math></inline-formula> piecewise expanding maps defined on the unit interval satisfying <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>λ</mi><mrow><mo>(</mo><msubsup><mi>T</mi><mi>ω</mi><mo>′</mo></msubsup><mo>)</mo></mrow><mo>=</mo><mo movablelimits="true" form="prefix">inf</mo><mrow><mo>|</mo><msubsup><mi>T</mi><mi>ω</mi><mo>′</mo></msubsup><mo>|</mo></mrow><mo>></mo><mn>2</mn></mrow></semantics></math></inline-formula>. As a principal tool of these studies, we use a coupling method for analyzing the coupling time of observables with bounded variation. |
|---|---|
| ISSN: | 2075-1680 |