Lévy stable distributions via associated integral transform

@article{Grska2012LvySD,
  title={L{\'e}vy stable distributions via associated integral transform},
  author={K. G{\'o}rska and K. Penson},
  journal={Journal of Mathematical Physics},
  year={2012},
  volume={53},
  pages={053302-053302}
}
We present a method of generation of exact and explicit forms of one-sided, heavy-tailed Levy stable probability distributions gα(x), 0 ⩽ x < ∞, 0 < α < 1. We demonstrate that the knowledge of one such a distribution gα(x) suffices to obtain exactly gαp(x), p = 2, 3, …  . Similarly, from known gα(x) and gβ(x), 0 < α, β < 1, we obtain gαβ(x). The method is based on the construction of the integral operator, called Levy transform, which implements the above operations. For α rational, α = l/k… Expand
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