Eur. Phys. J. B 20, 3-6 (2001)
https://doi.org/10.1007/BF01313905

Stochastic equations generating continuous multiplicative cascades

¹ Vrije Universiteit Brussel, Dept. of Fluid Mechanics, Pleinlaan 2, 1050 Brussels, Belgium
² LGIT, Université de Savoie Campus Scientifique, 73376 Le Bourget du Lac, Cedex, France

Corresponding author: ^a francois@stro.vub.ac.be

Received: 26 October 2000
Revised: 2 February 2001
Published online: 15 March 2001

Abstract

Discrete multiplicative turbulent cascades are described using a formalism involving infinitely divisible random measures. This permits to consider the continuous limit of a cascade developed on a continuum of scales, and to provide the stochastic equations defining such processes, involving infinitely divisible stochastic integrals. Causal evolution laws are also given. This gives the first general stochastic equations which generate continuous multifractal measures or processes.