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The Lamperti transformation for self-similar processes

Author

Listed:
  • Krzysztof Burnecki
  • Makoto Maejima
  • Aleksander Weron

Abstract

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 Science and Technology.
    • Handle: RePEc:wuu:wpaper:hsc9702
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    File URL: http://www.im.pwr.wroc.pl/~hugo/RePEc/wuu/wpaper/HSC_97_02.pdf
    File Function: Final version, 1997
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    Citations

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    Cited by:

    1. 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.
    2. Makoto Maejima & Ken-iti Sato, 1999. "Semi-Selfsimilar Processes," Journal of Theoretical Probability, Springer, vol. 12(2), pages 347-373, April.
    3. 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.
    4. Krzysztof Burnecki, 1998. "Self-similar models in risk theory," HSC Research Reports HSC/98/03, Hugo Steinhaus Center, Wroclaw University of Science and Technology.

    More about this item

    Keywords

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