Fractional probability
Fractional probability is a synthesis of
continuous probability and
fractional calculus. More precisely, it is a reformulation of the
fractional paradigm onto a rigorous foundation—a foundation of
counting and
measure which incorporates fractal sets into its inherent assumptions.
Topics includes:
- measure theory
- fractals
- 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.
- multifractals - The most natural structures.