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"&...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-11-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/12/1072 |
| _version_ | 1797382062945075200 |
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| author | Mohamed Abdelkader |
| author_facet | Mohamed Abdelkader |
| author_sort | Mohamed Abdelkader |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-08T21:01:00Z |
| format | Article |
| id | doaj.art-cb566b8c0eee494b8abd9009b84887a1 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-08T21:01:00Z |
| publishDate | 2023-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-cb566b8c0eee494b8abd9009b84887a12023-12-22T13:53:09ZengMDPI AGAxioms2075-16802023-11-011212107210.3390/axioms12121072Analysis of Correlation Bounds for Uniformly Expanding Maps on [0, 1]Mohamed Abdelkader0Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaIn 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.https://www.mdpi.com/2075-1680/12/12/1072decay of correlationsuniformly expanding mapsrandom dynamical systems |
| spellingShingle | Mohamed Abdelkader Analysis of Correlation Bounds for Uniformly Expanding Maps on [0, 1] Axioms decay of correlations uniformly expanding maps random dynamical systems |
| title | Analysis of Correlation Bounds for Uniformly Expanding Maps on [0, 1] |
| title_full | Analysis of Correlation Bounds for Uniformly Expanding Maps on [0, 1] |
| title_fullStr | Analysis of Correlation Bounds for Uniformly Expanding Maps on [0, 1] |
| title_full_unstemmed | Analysis of Correlation Bounds for Uniformly Expanding Maps on [0, 1] |
| title_short | Analysis of Correlation Bounds for Uniformly Expanding Maps on [0, 1] |
| title_sort | analysis of correlation bounds for uniformly expanding maps on 0 1 |
| topic | decay of correlations uniformly expanding maps random dynamical systems |
| url | https://www.mdpi.com/2075-1680/12/12/1072 |
| work_keys_str_mv | AT mohamedabdelkader analysisofcorrelationboundsforuniformlyexpandingmapson01 |