Continuous cascades in the wavelet space as models for synthetic turbulence
| Autor: | Jean-François Muzy |
|---|---|
| Přispěvatelé: | Université Pascal Paoli (UPP) |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Stochastic process
Statistical Physics Fluid Dynamics (physics.flu-dyn) FOS: Physical sciences Multifractal system Physics - Fluid Dynamics Grid 01 natural sciences Orthogonal basis [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph] 010305 fluids & plasmas Wavelet Physics - Data Analysis Statistics and Probability 0103 physical sciences Convergence (routing) Statistical physics Invariant (mathematics) 010306 general physics Data Analysis Statistics and Probability (physics.data-an) Continuous wavelet transform [PHYS.PHYS.PHYS-DATA-AN]Physics [physics]/Physics [physics]/Data Analysis Statistics and Probability [physics.data-an] Mathematics |
| Zdroj: | Physical Review E : Statistical, Nonlinear, and Soft Matter Physics Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2019, 99 (4), pp.042113. ⟨10.1103/PhysRevE.99.042113⟩ Phys.Rev.E Phys.Rev.E, 2019, 99 (4), pp.042113. ⟨10.1103/PhysRevE.99.042113⟩ |
| ISSN: | 1539-3755 1550-2376 |
| DOI: | 10.1103/PhysRevE.99.042113⟩ |
| Popis: | We introduce a wide family of stochastic processes that are obtained as sums of self-similar localized "waveforms" 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 $\cal W$-cascades introduced in the past by Arneodo, Bacry and Muzy using 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. 42 pages, 13 figures |
| Databáze: | OpenAIRE |
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