Multifractal

Lesson

Introduction
Multifractal theory
Hierarchy of singularities
- Statistical deception of multifractal processes
- Co-dimenion function c(g)
- Statistical moment function k(q)
- K(q) proprieties
- General proprieties of multifractal
- Conservative and non-conservative quantities
Multifractal and extremes
Universal multifractal model
Exercises
Conclusion

Statistical deception of multifractal processes

In probability theory and statistics , the moment of order of real random variable is a measure of the dispersion of this variable , for instance the standard deviation , the square root of central moment of order 2. The statistical order are:

$m_q \overset{\Delta}{=} E(X^r)$

Also, it can be described using its distribution function:

The practical importance of the distribution function is that it allows to calculate the probability of any interval :

$Pr(a \leqslant X < b) = f(b) - f(a)$

Distribution function of continuous random variable

In the following sections we will present the multifractal processes by describing their statistical characteristics.

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