Pierre Borgnat et al 2005 J. Phys. A: Math. Gen. 38 2081 doi:10.1088/0305-4470/38/10/002
Pierre Borgnat1, Pierre-Olivier Amblard2 and Patrick Flandrin1
Show affiliationsScale-invariant processes, and hereafter processes with broken versions of this symmetry, are studied by means of the Lamperti transformation, a one-to-one transformation linking stationary and self-similar processes. A general overview of the use of the transformation, and of the stationary generators it builds, is given for modelling and analysis of scale invariance. We put an emphasis on generalizations to non-strictly scale-invariant situations. The examples of discrete scale invariance and finite-size scale invariance are developed by means of the Lamperti transformation framework, and some specific examples of processes with these generalized symmetries are given.
Issue 10 (11 March 2005)
Received 20 October 2004, in final form 30 December 2004
Published 23 February 2005
Pierre Borgnat et al 2005 J. Phys. A: Math. Gen. 38 2081
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