Intermittency Expansions for Limit Lognormal Multifractals

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Abstract

The general intermittency expansion is developed for the probability distribution of the limit lognormal multifractal process introduced by Mandelbrot (in Rosenblatt M, Van Atta C (eds.) Statistical Models and Turbulence. Lecture Notes in Physics, vol. 12, p. 333. Springer, New York, 1972) and constructed explicitly by Bacry et al. (Phys Rev E 64:026103, 2001). The structure of expansion coefficients is shown to be determined solely by that of the Selberg integral. The coefficients are computed in terms of the values of the Riemann zeta function at positive integers. For application, an explicit formula for the negative integral moments of the process is given.

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