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Stochastic Discrete Scale Invariance

Abstract : A definition of stochastic discrete scale invariance (DSI) is proposed and its properties studied. It is shown how the Lamperti transformation, which transforms stationarity in self-similarity, is also a means to connect processes deviating from stationarity and processes which are not exactly scale invariant: in particular we interpret DSI as the image of cyclostationarity. This theoretical result is employed to introduce a multiplicative spectral representation of DSI processes based on the Mellin transform, and preliminar remarks are given about estimation issues.
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https://hal-ens-lyon.archives-ouvertes.fr/ensl-00175962
Contributor : Pierre Borgnat Connect in order to contact the contributor
Submitted on : Monday, October 1, 2007 - 8:33:51 PM
Last modification on : Wednesday, July 28, 2021 - 3:48:01 PM
Long-term archiving on: : Thursday, September 27, 2012 - 12:20:58 PM

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Pierre Borgnat, Patrick Flandrin, Pierre-Olivier Amblard. Stochastic Discrete Scale Invariance. IEEE Signal Processing Letters, Institute of Electrical and Electronics Engineers, 2002, 9 (6), pp.181-184. ⟨ensl-00175962⟩

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