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- W14519630 abstract "The analysis of the linearization effect in multifractal analysis, and hence of the estimation of moments for multifractal processes, is revisited borrowing concepts from the statistical physics of disordered systems, notably from the analysis of the so-called Random Energy Model. Considering a standard multifractal process (compound Poisson motion), chosen as a simple representative example, we show: i) the existence of a critical order qbeyond which moments, though finite, cannot be estimated thr ough empirical averages, irrespective of the sample size of the observatio n; ii) that multifractal exponents necessarily behave line arly in q, for q > q � . Tayloring the analysis conducted for the Random Energy Model to that of Compound Poisson motion, we provide explicative and quantitative predictions for the values of qand for the slope controlling the linear behavior of the mult ifractal exponents. These quantities are shown to be related only to the definition of the multifractal process and not to depend on the sample size of the observation. Monte-Carlo simulations, conducted over a large number of large sample size realizations of compound Poisson motion, comfort and extend these analyses." @default.
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- W14519630 date "2010-12-16" @default.
- W14519630 modified "2023-10-06" @default.
- W14519630 title "Linearization effect in multifractal analysis: Insights from Random Energy Model analysis" @default.
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