A Generalization of Multifractional Brownian Motion
In this article, some properties of multifractional Brownian motion (MFBM) are discussed. It is shown that it has persistence of signs long range dependence (LRD) and persistence of magnitudes LRD properties. A generalization called here <i>n</i>th order multifractional Brownian motion (...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-01-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/2/74 |
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| author | Neha Gupta Arun Kumar Nikolai Leonenko |
| author_facet | Neha Gupta Arun Kumar Nikolai Leonenko |
| author_sort | Neha Gupta |
| collection | DOAJ |
| description | In this article, some properties of multifractional Brownian motion (MFBM) are discussed. It is shown that it has persistence of signs long range dependence (LRD) and persistence of magnitudes LRD properties. A generalization called here <i>n</i>th order multifractional Brownian motion (<i>n</i>-MFBM) that allows to take the functional parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow></semantics></math></inline-formula> values in the range <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo>,</mo><mi>n</mi><mo>)</mo></mrow></semantics></math></inline-formula> is discussed. Two representations of the <i>n</i>-MFBM are given and their relationship with each other is obtained. |
| first_indexed | 2024-03-09T21:55:50Z |
| format | Article |
| id | doaj.art-82632c9190ce4befa30692ea6d4e2e17 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T21:55:50Z |
| publishDate | 2022-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-82632c9190ce4befa30692ea6d4e2e172023-11-23T19:58:47ZengMDPI AGFractal and Fractional2504-31102022-01-01627410.3390/fractalfract6020074A Generalization of Multifractional Brownian MotionNeha Gupta0Arun Kumar1Nikolai Leonenko2Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar 140001, IndiaDepartment of Mathematics, Indian Institute of Technology Ropar, Rupnagar 140001, IndiaCardiff School of Mathematics, Cardiff University, Senghennydd Road, Cardiff CF24 4AG, UKIn this article, some properties of multifractional Brownian motion (MFBM) are discussed. It is shown that it has persistence of signs long range dependence (LRD) and persistence of magnitudes LRD properties. A generalization called here <i>n</i>th order multifractional Brownian motion (<i>n</i>-MFBM) that allows to take the functional parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow></semantics></math></inline-formula> values in the range <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo>,</mo><mi>n</mi><mo>)</mo></mrow></semantics></math></inline-formula> is discussed. Two representations of the <i>n</i>-MFBM are given and their relationship with each other is obtained.https://www.mdpi.com/2504-3110/6/2/74multifractional Brownian motionlong range dependenceharmonizable representationHurst parameterHölder continuity |
| spellingShingle | Neha Gupta Arun Kumar Nikolai Leonenko A Generalization of Multifractional Brownian Motion Fractal and Fractional multifractional Brownian motion long range dependence harmonizable representation Hurst parameter Hölder continuity |
| title | A Generalization of Multifractional Brownian Motion |
| title_full | A Generalization of Multifractional Brownian Motion |
| title_fullStr | A Generalization of Multifractional Brownian Motion |
| title_full_unstemmed | A Generalization of Multifractional Brownian Motion |
| title_short | A Generalization of Multifractional Brownian Motion |
| title_sort | generalization of multifractional brownian motion |
| topic | multifractional Brownian motion long range dependence harmonizable representation Hurst parameter Hölder continuity |
| url | https://www.mdpi.com/2504-3110/6/2/74 |
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