The Annals of Applied Probability

Lp-variations for multifractal fractional random walks

Carenne Ludeña

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A multifractal random walk (MRW) is defined by a Brownian motion subordinated by a class of continuous multifractal random measures M[0, t], 0≤t≤1. In this paper we obtain an extension of this process, referred to as multifractal fractional random walk (MFRW), by considering the limit in distribution of a sequence of conditionally Gaussian processes. These conditional processes are defined as integrals with respect to fractional Brownian motion and convergence is seen to hold under certain conditions relating the self-similarity (Hurst) exponent of the fBm to the parameters defining the multifractal random measure M. As a result, a larger class of models is obtained, whose fine scale (scaling) structure is then analyzed in terms of the empirical structure functions. Implications for the analysis and inference of multifractal exponents from data, namely, confidence intervals, are also provided.

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Ann. Appl. Probab., Volume 18, Number 3 (2008), 1138-1163.

First available in Project Euclid: 26 May 2008

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Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems 60G57: Random measures 60K40: Other physical applications of random processes 62F10: Point estimation
Secondary: 60G15: Gaussian processes 60G18: Self-similar processes 60E07: Infinitely divisible distributions; stable distributions

Fractional Brownian motion multifractal random measures multifractal random walks L^p-variations linearization effect scaling phenomena


Ludeña, Carenne. L p -variations for multifractal fractional random walks. Ann. Appl. Probab. 18 (2008), no. 3, 1138--1163. doi:10.1214/07-AAP483.

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