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February 2014 Estimating the scaling function of multifractal measures and multifractal random walks using ratios
Carenne Ludeña, Philippe Soulier
Bernoulli 20(1): 334-376 (February 2014). DOI: 10.3150/12-BEJ489

Abstract

In this paper, we prove central limit theorems for bias reduced estimators of the structure function of several multifractal processes, namely mutiplicative cascades, multifractal random measures, multifractal random walk and multifractal fractional random walk as defined by Ludeña [Ann. Appl. Probab. 18 (2008) 1138–1163]. Previous estimators of the structure functions considered in the literature were severely biased with a logarithmic rate of convergence, whereas the estimators considered here have a polynomial rate of convergence.

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Carenne Ludeña. Philippe Soulier. "Estimating the scaling function of multifractal measures and multifractal random walks using ratios." Bernoulli 20 (1) 334 - 376, February 2014. https://doi.org/10.3150/12-BEJ489

Information

Published: February 2014
First available in Project Euclid: 22 January 2014

zbMATH: 06282554
MathSciNet: MR3160585
Digital Object Identifier: 10.3150/12-BEJ489

Rights: Copyright © 2014 Bernoulli Society for Mathematical Statistics and Probability

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Vol.20 • No. 1 • February 2014
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