Electronic Journal of Probability

Self-regulating processes

Olivier Barrière, Antoine Echelard, and Jacques Lévy Véhel

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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.

Article information

Electron. J. Probab., Volume 17 (2012), paper no. 103, 30 pp.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G17: Sample path properties
Secondary: 60G22: Fractional processes, including fractional Brownian motion 26A16: Lipschitz (Hölder) classes

Hölder regularity Weierstrass function multifractional Brownian motion self-regulating processes

This work is licensed under aCreative Commons Attribution 3.0 License.


Barrière, Olivier; Echelard, Antoine; Lévy Véhel, Jacques. Self-regulating processes. Electron. J. Probab. 17 (2012), paper no. 103, 30 pp. doi:10.1214/EJP.v17-2010. https://projecteuclid.org/euclid.ejp/1465062425

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