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Fractional Processes and Fractional-Order Signal Processing pp 49–76Cite as

Constant-Order Fractional Processes

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Part of the book series: Signals and Communication Technology ((SCT))

Abstract

Chapter 3 deals with the constant-order fractional processes and the Hurst parameter estimators evaluation. A fractional process with a constant long memory parameter can be regarded as the output signal of a fractional-order system driven by white Gaussian noise. Typical constant-order fractional processes including fractional Brownian motion, fractional Gaussian noise, fractional stable motion, and fractional stable noise. A constant-order fractional process can be characterized by its long memory parameter H, the Hurst parameter or Hurst exponent. In this chapter, long-range dependent processes and Hurst parameter estimators are introduced. Furthermore, the robustness and the accuracy of twelve Hurst parameter estimators are extensively studied.

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Authors and Affiliations

  1. School of Electronic and Information Engineering, Dalian Jiaotong University, Dalian, People’s Republic of China

    Hu Sheng

  2. Department of Electrical and Computer Engineering, CSOIS, Utah State University, Old Main Hill 4160, Logan, UT, 84322-4120, USA

    YangQuan Chen

  3. School of Electronic and Information Engineering, Dalian University of Technology, Dalian, People’s Republic of China

    TianShuang Qiu

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  1. Hu Sheng
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  2. YangQuan Chen
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  3. TianShuang Qiu
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Correspondence to Hu Sheng .

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© 2012 Springer-Verlag London Limited

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Sheng, H., Chen, Y., Qiu, T. (2012). Constant-Order Fractional Processes. In: Fractional Processes and Fractional-Order Signal Processing. Signals and Communication Technology. Springer, London. https://doi.org/10.1007/978-1-4471-2233-3_3

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  • DOI: https://doi.org/10.1007/978-1-4471-2233-3_3

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-2232-6

  • Online ISBN: 978-1-4471-2233-3

  • eBook Packages: EngineeringEngineering (R0)

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