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Stochastic invariances and Lamperti transformations for Stochastic Processes

Abstract : Scale-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.
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Contributor : Pierre Borgnat Connect in order to contact the contributor
Submitted on : Monday, October 1, 2007 - 8:22:54 PM
Last modification on : Wednesday, July 28, 2021 - 3:48:01 PM
Long-term archiving on: : Thursday, September 27, 2012 - 12:20:25 PM


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  • HAL Id : ensl-00175960, version 1



Pierre Borgnat, Pierre-Olivier Amblard, Patrick Flandrin. Stochastic invariances and Lamperti transformations for Stochastic Processes. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2005, pp.2081-2101. ⟨ensl-00175960⟩



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