Definition, properties and wavelet analysis of multiscale fractional Brownian motionReportar como inadecuado




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1 SAMOS - Statistique Appliquée et MOdélisation Stochastique 2 CES - Centre d-économie de la Sorbonne 3 PAS LMBP - Laboratoire de Mathématiques Blaise Pascal

Abstract : In some applications, for instance finance, biomechanics, turbulence or internet traffic, it is relevant to model data with a generalization of a fractional Brownian motion for which the Hurst parameter $H$ is depending on the frequency. In this contribution, we describe the multiscale fractional Brownian motions which present a parameter $H$ as a piecewise constant function of the frequency. We provide the main properties of these processes: long-memory and smoothness of the paths. Then we propose a statistical method based on wavelet analysis to estimate the different parameters and prove a functional Central Limit Theorem satisfied by the empirical variance of the wavelet coefficients.

Keywords : Fractional Brownian motion Long-range dependence Path regularity Self-similarity Wavelet analysis Functional Central Limit Theorem





Autor: Jean-Marc Bardet - Pierre, Raphael Bertrand -

Fuente: https://hal.archives-ouvertes.fr/



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