Spectral Representation and Structure of Stable Self-Similar Processes

  • K. Burnecki
  • J. Rosiński
  • A. Weron
Part of the Trends in Mathematics book series (TM)


In this paper we establish a spectral representation of any symmetric stable self-similar process in terms of multiplicative flows and cocycles. A structure of this class of self-similar processes is studied. 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. This decomposition is illustrated by graphical presentation of corresponding kernels of their spectral representations.


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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • K. Burnecki
    • 1
  • J. Rosiński
    • 2
  • A. Weron
    • 1
  1. 1.Hugo Steinhaus Center for Stochastic MethodsTechnical UniversityWroclawPoland
  2. 2.Mathematics DepartmentUniversity of TennesseeKnoxvilleUSA

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