Analytic multivariate generating function for random multiplicative cascade processes

Abstract

We have found an analytic expression for the multivariate generating function governing all n-point statistics of random multiplicative cascade processes. The variable appropriate for this generating function is the logarithm of the energy density, ln epsilon, rather than epsilon itself. All cumulant statistics become sums over derivatives of ``branching generating functions'' which are Laplace transforms of the splitting functions and completely determine the cascade process. We show that the branching generating function is a generalization of the multifractal mass exponents. Two simple models from fully developed turbulence illustrate the new formalism.

REVTeX, 4 pages, 2 PostScript figs, submitted to PRL

References in corpus (2)

• The multifractal nature of turbulent energy dissipation
• Probing Hierarchical Clustering by Scale-Scale Correlations of Wavelet Coefficients

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