Fractional Gaussian Noise: Projections, Prediction, Norms
We examine the one-sided and two-sided (bilateral) projections of an element of fractional Gaussian noise onto its neighboring elements. We establish several analytical results and conduct a numerical study to analyze the behavior of the coefficients of these projections as functions of the Hurst in...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-06-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/7/428 |
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| _version_ | 1850077906590498816 |
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| author | Iryna Bodnarchuk Yuliya Mishura Kostiantyn Ralchenko |
| author_facet | Iryna Bodnarchuk Yuliya Mishura Kostiantyn Ralchenko |
| author_sort | Iryna Bodnarchuk |
| collection | DOAJ |
| description | We examine the one-sided and two-sided (bilateral) projections of an element of fractional Gaussian noise onto its neighboring elements. We establish several analytical results and conduct a numerical study to analyze the behavior of the coefficients of these projections as functions of the Hurst index and the number of neighboring elements used for the projection. We derive recurrence relations for the coefficients of the two-sided projection. Additionally, we explore the norms of both types of projections. Certain special cases are investigated in greater detail, both theoretically and numerically. |
| format | Article |
| id | doaj-art-edbe77293ced4fb6b4da365073aede9d |
| institution | DOAJ |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-edbe77293ced4fb6b4da365073aede9d2025-08-20T02:45:42ZengMDPI AGFractal and Fractional2504-31102025-06-019742810.3390/fractalfract9070428Fractional Gaussian Noise: Projections, Prediction, NormsIryna Bodnarchuk0Yuliya Mishura1Kostiantyn Ralchenko2Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, 64/13 Volodymyrska St., 01601 Kyiv, UkraineDepartment of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, 64/13 Volodymyrska St., 01601 Kyiv, UkraineDepartment of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, 64/13 Volodymyrska St., 01601 Kyiv, UkraineWe examine the one-sided and two-sided (bilateral) projections of an element of fractional Gaussian noise onto its neighboring elements. We establish several analytical results and conduct a numerical study to analyze the behavior of the coefficients of these projections as functions of the Hurst index and the number of neighboring elements used for the projection. We derive recurrence relations for the coefficients of the two-sided projection. Additionally, we explore the norms of both types of projections. Certain special cases are investigated in greater detail, both theoretically and numerically.https://www.mdpi.com/2504-3110/9/7/428fractional Brownian motionfractional Gaussian noisecoefficients of projectionprediction coefficients<i>L</i><sub>2</sub>-normautocovariance function |
| spellingShingle | Iryna Bodnarchuk Yuliya Mishura Kostiantyn Ralchenko Fractional Gaussian Noise: Projections, Prediction, Norms Fractal and Fractional fractional Brownian motion fractional Gaussian noise coefficients of projection prediction coefficients <i>L</i><sub>2</sub>-norm autocovariance function |
| title | Fractional Gaussian Noise: Projections, Prediction, Norms |
| title_full | Fractional Gaussian Noise: Projections, Prediction, Norms |
| title_fullStr | Fractional Gaussian Noise: Projections, Prediction, Norms |
| title_full_unstemmed | Fractional Gaussian Noise: Projections, Prediction, Norms |
| title_short | Fractional Gaussian Noise: Projections, Prediction, Norms |
| title_sort | fractional gaussian noise projections prediction norms |
| topic | fractional Brownian motion fractional Gaussian noise coefficients of projection prediction coefficients <i>L</i><sub>2</sub>-norm autocovariance function |
| url | https://www.mdpi.com/2504-3110/9/7/428 |
| work_keys_str_mv | AT irynabodnarchuk fractionalgaussiannoiseprojectionspredictionnorms AT yuliyamishura fractionalgaussiannoiseprojectionspredictionnorms AT kostiantynralchenko fractionalgaussiannoiseprojectionspredictionnorms |