Title :
Stochastic discrete scale invariance
Author :
Borgnat, Pierre ; Flandrin, Patrick ; Amblard, Pierre-Olivier
Author_Institution :
Lab. de Phys., Ecole Normale Superieure de Lyon, France
fDate :
6/1/2002 12:00:00 AM
Abstract :
A definition of stochastic discrete scale invariance (DSI) is proposed and its properties studied. It is shown how the Lamperti (1962) 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 preliminary remarks are given about estimation issues.
Keywords :
fractals; set theory; signal representation; spectral analysis; stochastic processes; transforms; Lamperti transformation; Mellin transform; cyclostationarity; deterministic fractal set; multiplicative spectral representation; self-similarity; stochastic discrete scale invariance; Discrete transforms; Earthquakes; Equations; Fractals; Joining processes; Proposals; Random variables; Stochastic processes; Telecommunication traffic;
Journal_Title :
Signal Processing Letters, IEEE
DOI :
10.1109/LSP.2002.800504
