Abstract.
New multiplicative and statistically self-similar measures μ are defined on ℝ as limits of measure-valued martingales. Those martingales are constructed by multiplying random functions attached to the points of a statistically self-similar Poisson point process defined in a strip of the plane. Several fundamental problems are solved, including the non-degeneracy and the multifractal analysis of μ. On a bounded interval, the positive and negative moments of diverge under broad conditions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Additional information
First received: 14 September 1999 / Resubmited: 27 June 2001 / Revised version: 30 May 2002 / Published online: 30 September 2002
Mathematics Subject Classification (2002): 28A80, 60G18, 60G44, 60G55, 60G57
Key words or phrases: Random measures – Multifractal analysis – Continuous time martingales – Statistically self-similar Poisson point processes
Rights and permissions
About this article
Cite this article
Barral, J., Mandelbrot, B. Multifractal products of cylindrical pulses. Probab Theory Relat Fields 124, 409–430 (2002). https://doi.org/10.1007/s004400200220
Issue Date:
DOI: https://doi.org/10.1007/s004400200220