Analytic multivariate generating function for random multiplicative cascade processes

Details Analytic multivariate generating function for random multiplicative cascade processes Analytic multivariate generating function for random multiplicative cascade processes

1998-04-13

arxiv.org/abs/chao-dyn/9804024v1

Nonlinear Sciences

Chaotic Dynamics

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

Scientific paper

10.1103/PhysRevLett.80.5333

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.

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