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2012 Self-regulating processes
Olivier Barrière, Antoine Echelard, Jacques Lévy Véhel
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Electron. J. Probab. 17: 1-30 (2012). DOI: 10.1214/EJP.v17-2010


We construct functions and stochastic processes for which a functional relation holds between amplitude and local regularity, as measured by the pointwise or local Hölder exponent. We consider in particular functions and processes built by extending Weierstrass function, multifractional Brownian motion and the Lévy 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 first step in the development of a theory for such self-regulating processes.


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Olivier Barrière. Antoine Echelard. Jacques Lévy Véhel. "Self-regulating processes." Electron. J. Probab. 17 1 - 30, 2012.


Accepted: 16 December 2012; Published: 2012
First available in Project Euclid: 4 June 2016

zbMATH: 1284.60076
MathSciNet: MR3005721
Digital Object Identifier: 10.1214/EJP.v17-2010

Primary: 60G17
Secondary: 26A16 , 60G22

Keywords: Hölder regularity , Multifractional Brownian motion , self-regulating processes , Weierstrass function


Vol.17 • 2012
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