Probabilistic fractals

A. Cashes, J. Mai, W. von Niessen. A Monte Carlo study of the CO oxidation on probabilistic fractals. J Chem Phys 99 3082-3091, 1993. 

In some cases, such values can be considered to be probabilistic fractals. For a discussion of this problem, see the review of Baveye and Boast [6] and the references quoted therein, in addition to Chapter 2 in this book. 

Nicolis, G. Gaspard, P. 1994. Toward a Probabilistic Approach to Complex Systems, Chaos, Solitions Fractals 4, 41—57. 

But power-law distributions may lack any characteristic scale. This property prevented the use of power-law distributions in the natural sciences until mathematical introduction of Levy s new probabilistic concepts and the physical introduction of new scaling concepts for thermodynamic functions and correlation functions (see ref. [40]). In financial markets, invariance of time scales means that even a stock expert cannot distinguish in a time series analysis if the charts are, for example, daily, weekly, or monthly. These charts are statistically self-similar or fractal. 

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