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.Comment: REVTeX, 4 pages, 2 PostScript figs, submitted to PR
