Uniform convergence for complex [0, 1]-martingales

Abstract : 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.
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The Annals of Applied Probability : an official journal of the institute of mathematical statistics, The Institute of Mathematical Statistics, 2010, 20 (4), pp.1205-1218. 〈10.1214/09-AAP664〉
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Soumis le : jeudi 21 février 2013 - 14:52:36
Dernière modification le : vendredi 25 mai 2018 - 12:02:05

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Julien Barral, Xiong Jin, Benoît Mandelbrot. Uniform convergence for complex [0, 1]-martingales. The Annals of Applied Probability : an official journal of the institute of mathematical statistics, The Institute of Mathematical Statistics, 2010, 20 (4), pp.1205-1218. 〈10.1214/09-AAP664〉. 〈hal-00793058〉

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