Spectral representation and structure of self-similar processes
AbstractIn 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.
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Bibliographic InfoPaper provided by Hugo Steinhaus Center, Wroclaw University of Technology in its series HSC Research Reports with number HSC/97/03.
Length: 17 pages
Date of creation: 1997
Date of revision:
Publication status: Published in I.Karatzas, B.Rajput and M.Taqqu (eds.), Stochastic Processes and Related Topics, Birhauser, Boston (1998) 1-14.
Self-similar process; Stable distribution; Lamperti transformation;
Find related papers by JEL classification:
- C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
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- 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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