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.
Complete list of metadatas

https://hal-ens-lyon.archives-ouvertes.fr/ensl-00175960
Contributor : Pierre Borgnat <>
Submitted on : Monday, October 1, 2007 - 8:22:54 PM
Last modification on : Friday, September 6, 2019 - 3:00:06 PM
Long-term archiving on : Thursday, September 27, 2012 - 12:20:25 PM

Files

scaleInv_Lamperti_rev.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : ensl-00175960, version 1

Collections

Citation

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⟩

Share

Metrics

Record views

314

Files downloads

137