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• W2905474694 abstract "We introduce a wide family of stochastic processes that are obtained as sums of self-similar localized ``wave forms'' with multiplicative intensity in the spirit of the Richardson cascade picture of turbulence. We establish the convergence and the minimum regularity of our construction. We show that its continuous wavelet transform is characterized by stochastic self-similarity and multifractal scaling properties. This model constitutes a stationary, ``grid free'' extension of $mathcal{W}$ cascades introduced in the past by Arneodo, Bacry, and Muzy using a wavelet orthogonal basis. Moreover, our approach generically provides multifractal random functions that are not invariant by time reversal and therefore is able to account for skewed multifractal models and for the so-called ``leverage effect.'' In that respect, it can be well suited to providing synthetic turbulence models or to reproducing the main observed features of asset price fluctuations in financial markets." @default.
• W2905474694 created "2018-12-22" @default.
• W2905474694 creator A5059295872 @default.
• W2905474694 date "2019-04-10" @default.
• W2905474694 modified "2023-10-07" @default.
• W2905474694 title "Continuous cascades in the wavelet space as models for synthetic turbulence" @default.
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• W2905474694 doi "https://doi.org/10.1103/physreve.99.042113" @default.
• W2905474694 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/31108704" @default.
• W2905474694 hasPublicationYear "2019" @default.
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