Lévy Stable Distributions & α-Stable Processes

Generalized CLT: stable laws, fat tails, superdiffusion

Parameters

Theory

φ(t) = exp(iμt - γ|t|^α(1+iβsgn(t)Φ))
α=2: Gaussian (finite variance)
α<2: power tail P(X>x)~x^(-α)
MSD: ⟨x²(t)⟩ ~ t^(2/α) (superdiff)

Statistics