Fractional probability

Fractional probability is a sythesis of continuous probability and fractional calculus. More precisely, it is a reassertion/reformulation of the grounds of the fractional paradigm onto a rigourous foundation—a foundation of counting[?] and measure which incorporates fractal sets[?] into its inherent assumptions. (For whereas mathematics is concerned, the theory of discrete probability is the theory of counting, and the theory of continuous probability is the theory of measure.)

Topics includes:

measure theory - The bricks and mortor of the whole beast.

fractal sets[?]

fractional-order probability distributions[?] - This is the generalization/extension of fundamental probability distributions/densities to arbitrary dimension. The generalizations are in most cases quite trivial mathematically, such as changing the range of an exponent from natural numbers to complex numbers. However, more explanation is demanded, and provided, for the development of geometric intuition.

fractional brownian motion[?]

non-gaussian diffusion[?]

Related topics include:

fractional paradigm - The mother topic.

fractional calculus - Integration on these sets. This is built on top of the current subject, and pedagogically follows.

fractals - The origin of it all.

multifractals[?] - The most natural, and in many ways beautiful, structures. These are the ideal material of the final development of this field.

Note: I have asserted this categorization and thereby proposed this field in an attempt to remedy certain shortcomings of the fractional paradigm. To the extent of my knowledge, the idea of this field is novel and non-redundant. The motivation for this categorization is discussed briefly on my page. I concede that it is not at this point canonical, but I assure you that if you bear with me, it will justify it's place. It is a rigourous discussion, and it has far more substantial backing than many accepted topics on this encyclopedia, which are boorishly trivial. (such as pop-culture)