UNIFORM CONVERGENCE FOR COMPLEX [0,1]-MARTINGALES

• 成果类型: Article
• 署名作者: Barral, Julien; Jin, Xiong; Mandelbrot, Benoit
• 署名单位: Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris 13; Inria; Yale University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/09-AAP664
• 发表日期: 2010
• 页码: 1205-1218
• 关键词: multifractal measures; martingales; cascades; PRODUCTS; time

摘要

Positive T-martingales were developed as a general framework that extends the positive measure-valued martingales and are meant to model intermittent turbulence. We extend their scope by allowing the martingale to take complex values. We focus on martingales constructed on the interval T = [0, 1] and replace random measures by random functions. We specify a large class of such martingales for which we provide a general sufficient condition for almost sure uniform convergence to a nontrivial limit. Such a limit yields new examples of naturally generated multifractal processes that may be of use in multifractal signals modeling.