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Revisiting fractional Gaussian noise

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  • Li, Ming
  • Sun, Xichao
  • Xiao, Xi

Abstract

The contributions given in this article are mainly in two folds with regard to the fractional Gaussian noise of the Weyl type. The first one is to present a complete form of fGn, which is taken as the output of a fractional-order filter driven by white noise. The second is to propose the analytic expressions of the impulse response function and the frequency transfer function of that fractional-order filter. We also give an expression of the fractional Brownian motion of the Weyl type as a consequence of the present fGn. Besides, we suggest that the statistical dependences of fGn may be described based on the frequency transfer function or the impulse response function of the fractional-order filter.

Suggested Citation

  • Li, Ming & Sun, Xichao & Xiao, Xi, 2019. "Revisiting fractional Gaussian noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 56-62.
    • Handle: RePEc:eee:phsmap:v:514:y:2019:i:c:p:56-62
    DOI: 10.1016/j.physa.2018.09.008
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    References listed on IDEAS

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    1. Xichao Sun & Ming Li & Wei Zhao, 2018. "Moderate Deviations for Stochastic Fractional Heat Equation Driven by Fractional Noise," Complexity, Hindawi, vol. 2018, pages 1-17, July.
    2. Eab, Chai Hok & Lim, S.C., 2018. "Ornstein–Uhlenbeck process with fluctuating damping," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 790-803.
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    4. Muniandy, S.V. & Lim, S.C. & Murugan, R., 2001. "Inhomogeneous scaling behaviors in Malaysian foreign currency exchange rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 301(1), pages 407-428.
    5. Cattani, Carlo & Ciancio, Armando, 2016. "On the fractal distribution of primes and prime-indexed primes by the binary image analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 222-229.
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    Cited by:

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