Multifractal

Co-dimenion function c(g)

The singularities are defined , we focus on their theoretical probability laws through the concept of the co-dimension function . In the genral case , the probability distribution function and the distribution function depend on the scale ratio . In the case of multifractal , they take a particular form.

a process is called multifractal if the function follows the law described by:

Pr(\varepsilon_\lambda \geqslant \lambda^{\overline{\gamma}}) \approx \lambda^{-c(\overline{\gamma})}

According to the figure in the above section, one can write:

Pr(\gamma \geqslant \lambda^{\overline{\gamma}}) \approx \lambda^{-c(\overline{\gamma})}

can be obtained by plotting the above equation in log-log plot.

Shape of C(g) function

It represents the logarithm of the probability of exceeding singularities and integrates information at all scales.

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