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The Lamperti transformation for self-similar processes


  • Krzysztof Burnecki
  • Makoto Maejima
  • Aleksander Weron


In this paper we establish the uniqueness of the Lamperti transformation leading from self-similar to stationary processes, and conversely. We discuss alpha-stable processes, which allow to understand better the difference between the Gaussian and non-Gaussian cases. As a by-product we get a natural construction of two distinct alpha-stable Ornstein–Uhlenbeck processes via the Lamperti transformation for 0

Suggested Citation

  • Krzysztof Burnecki & Makoto Maejima & Aleksander Weron, 1997. "The Lamperti transformation for self-similar processes," HSC Research Reports HSC/97/02, Hugo Steinhaus Center, Wroclaw University of Technology.
  • Handle: RePEc:wuu:wpaper:hsc9702

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    Cited by:

    1. Fernández-Martínez, M. & Sánchez-Granero, M.A. & Trinidad Segovia, J.E., 2013. "Measuring the self-similarity exponent in Lévy stable processes of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(21), pages 5330-5345.
    2. Magdziarz, Marcin, 2009. "Correlation cascades, ergodic properties and long memory of infinitely divisible processes," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3416-3434, October.
    3. 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


    Lamperti transformation; Self-similar process; Stationary process; Stable distribution;

    JEL classification:

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


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