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Spectral representation and structure of self-similar processes


  • Krzysztof Burnecki
  • Jan Rosinski
  • Aleksander Weron


In this paper we establish a spectral representation of any symmetric stable self-similar process in terms of multiplicative flows and cocycles. Applying the Lamperti transformation we obtain a unique decomposition of a symmetric stable self-similar process into three independent parts: mixed fractional motion, harmonizable and evanescent.

Suggested Citation

  • Krzysztof Burnecki & Jan Rosinski & Aleksander Weron, 1997. "Spectral representation and structure of self-similar processes," HSC Research Reports HSC/97/03, Hugo Steinhaus Center, Wroclaw University of Technology.
  • Handle: RePEc:wuu:wpaper:hsc9703

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    File Function: Final version, 1997
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    Cited by:

    1. Wang, Yizao & Stoev, Stilian A., 2010. "On the association of sum- and max-stable processes," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 480-488, March.
    2. Krzysztof Burnecki, 1998. "Self-similar models in risk theory," HSC Research Reports HSC/98/03, Hugo Steinhaus Center, Wroclaw University of Technology.

    More about this item


    Self-similar process; Stable distribution; Lamperti transformation;
    All these keywords.

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions


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