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The Lamperti transformation for self-similar processes

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Author Info

  • 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

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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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Bibliographic Info

Paper provided by Hugo Steinhaus Center, Wroclaw University of Technology in its series HSC Research Reports with number HSC/97/02.

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Length: 16 pages
Date of creation: 1997
Date of revision:
Publication status: Published in Yokohama Mathematical Journal 44 (1997) 25-42.
Handle: RePEc:wuu:wpaper:hsc9702

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Related research

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

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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. Krzysztof Burnecki, 1998. "Self-similar models in risk theory," HSC Research Reports HSC/98/03, Hugo Steinhaus Center, Wroclaw University of Technology.

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