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This paper is concerned with Mandelbrot's stochastic cascade measures. The problems of (i) scaling exponents of structure functions of the measure, τ(#), and (ii) multifractal dimensions are considered for cascades with a generator vector (wι w c ) of the general type. These problems were previously studied for independent strongly bounded variables w l : 0 < a < w/ ^ c. Consequently, a broad class of models used in applications, including Kolmogorov's log-normal model in turbulence, log-stable "universal" cascades in atmospheric dynamics, has not been covered. Roughly speaking, problems (i), (ii) are here solved under the condition that the scaling exists; the τ-function is calculated for all arguments (previously this was done for positive q) and a new effect emerges: the τ-function can generally involve discontinuities in the first derivative as well as in the second.

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S U M M A R YT h e problem of aftershock identification in earthquake catalogues is studied. Some empirical methods are considered and quantitavely analysed.Game theory approach is applied t o formulate the problem allowing a whole class of optimal methods of aftershock identification. Each method is optimal depending on the goals and gives the best trade-off between the number of missed aftershocks and the number of incorrectly identified ones. Some illustrations of the new approach to the aftershock identification problem are presented.