## Electronic Journal of Probability

### Self-regulating processes

#### 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 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

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

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

https://projecteuclid.org/euclid.ejp/1465062425

Digital Object Identifier
doi:10.1214/EJP.v17-2010

Mathematical Reviews number (MathSciNet)
MR3005721

Zentralblatt MATH identifier
1284.60076

Rights

#### Citation

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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