Stochastic processes with finite size scale invariance

Pierre-Olivier Amblard; Pierre Borgnat; Patrick Flandrin

doi:10.1117/12.497411

7 May 2003 Stochastic processes with finite size scale invariance

Pierre-Olivier Amblard, Pierre Borgnat, Patrick Flandrin

Proceedings Volume 5114, Noise in Complex Systems and Stochastic Dynamics; (2003) https://doi.org/10.1117/12.497411
Event: SPIE's First International Symposium on Fluctuations and Noise, 2003, Santa Fe, New Mexico, United States

Abstract

We present a theory of stochastic processes that are finite size scale invariant. Such processes are invariant under generalized dilations that operate on bounded ranges of scales and amplitudes. We recall here the theory of deterministic finite size scale invariance, and introduce an operator called Lamperti transform that makes equivalent generalized dilations and translations. This operator is then used to defined finite size scale invariant processes as image of stationary processes. The example of the Brownian motion is presented is some details to illustrate the definitions. We further extend the theory to the case of finite size scale invariant processes with stationary increments.

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Pierre-Olivier Amblard, Pierre Borgnat, and Patrick Flandrin "Stochastic processes with finite size scale invariance", Proc. SPIE 5114, Noise in Complex Systems and Stochastic Dynamics, (7 May 2003); https://doi.org/10.1117/12.497411

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