Spectral Representation and Simulation of Fractional Brownian Motion
This paper gives a new representation for the fractional Brownian motion that can be applied to simulate this self-similar random process in continuous time. Such a representation is based on the spectral form of mathematical description and the spectral method. The Legendre polynomials are used as...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-01-01
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| Series: | Computation |
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| Online Access: | https://www.mdpi.com/2079-3197/13/1/19 |
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| _version_ | 1832588790929031168 |
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| author | Konstantin Rybakov |
| author_facet | Konstantin Rybakov |
| author_sort | Konstantin Rybakov |
| collection | DOAJ |
| description | This paper gives a new representation for the fractional Brownian motion that can be applied to simulate this self-similar random process in continuous time. Such a representation is based on the spectral form of mathematical description and the spectral method. The Legendre polynomials are used as the orthonormal basis. The paper contains all the necessary algorithms and their theoretical foundation, as well as the results of numerical experiments. |
| format | Article |
| id | doaj-art-afbd88b6d08f46a080c296741d0201f0 |
| institution | Kabale University |
| issn | 2079-3197 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Computation |
| spelling | doaj-art-afbd88b6d08f46a080c296741d0201f02025-01-24T13:27:49ZengMDPI AGComputation2079-31972025-01-011311910.3390/computation13010019Spectral Representation and Simulation of Fractional Brownian MotionKonstantin Rybakov0Independent Researcher, 127299 Moscow, RussiaThis paper gives a new representation for the fractional Brownian motion that can be applied to simulate this self-similar random process in continuous time. Such a representation is based on the spectral form of mathematical description and the spectral method. The Legendre polynomials are used as the orthonormal basis. The paper contains all the necessary algorithms and their theoretical foundation, as well as the results of numerical experiments.https://www.mdpi.com/2079-3197/13/1/19approximationfractional Brownian motionLegendre polynomialssimulationspectral characteristicspectral form of mathematical description |
| spellingShingle | Konstantin Rybakov Spectral Representation and Simulation of Fractional Brownian Motion Computation approximation fractional Brownian motion Legendre polynomials simulation spectral characteristic spectral form of mathematical description |
| title | Spectral Representation and Simulation of Fractional Brownian Motion |
| title_full | Spectral Representation and Simulation of Fractional Brownian Motion |
| title_fullStr | Spectral Representation and Simulation of Fractional Brownian Motion |
| title_full_unstemmed | Spectral Representation and Simulation of Fractional Brownian Motion |
| title_short | Spectral Representation and Simulation of Fractional Brownian Motion |
| title_sort | spectral representation and simulation of fractional brownian motion |
| topic | approximation fractional Brownian motion Legendre polynomials simulation spectral characteristic spectral form of mathematical description |
| url | https://www.mdpi.com/2079-3197/13/1/19 |
| work_keys_str_mv | AT konstantinrybakov spectralrepresentationandsimulationoffractionalbrownianmotion |