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.
Citation
Julien Barral. Xiong Jin. Benoît Mandelbrot. "Uniform convergence for complex [0, 1]-martingales." Ann. Appl. Probab. 20 (4) 1205 - 1218, August 2010. https://doi.org/10.1214/09-AAP664
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