Abstract : We construct functions and stochastic processes for which a functional relation holds between amplitude and local regularity, as measured by the pointwise or local Holder exponent. We consider in particular functions and processes built by extending Weierstrass function, multifractional Brownian motion and the L evy construction of Brownian motion. Such processes have recently proved to be relevant models in various applications. The aim of this work is to provide a theoretical background to these studies and to provide a rst step in the development of a theory for such self-regulating processes.
Type de document :
Article dans une revue
Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2012, 〈10.1214/EJP.v17-2010〉
https://hal.inria.fr/hal-00749742
Contributeur : Lisandro Fermin
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Soumis le : jeudi 8 novembre 2012 - 11:51:37
Dernière modification le : mercredi 19 décembre 2018 - 15:02:04
Document(s) archivé(s) le : samedi 17 décembre 2016 - 09:05:23
Olivier Barriere, Antoine Echelard, Jacques Lévy Véhel. Self-Regulating Processes. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2012, 〈10.1214/EJP.v17-2010〉. 〈hal-00749742〉
