One-sided Lévy stable distributions

Abstract

In this paper, we show new representations of one-sided Lévy stable distributions for irrational Lévy indices of the type ${\left(\frac{p}{q}\right)}^{\frac{l_2}{l_1}}$ which are not covered in \cite{pg1} : for rational Lévy indices. Furthermore, other equivalent representations for a distribution of a rational Lévy index is described. We also give a simplest proof for the formulae which cover the cases for rational Lévy indices. Finally we introduce the concepts of Lévy smashing and Lévy-smashed gamma stochastic processes.

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References in corpus (2)

• Exact and explicit probability densities for one-sided Levy stable distributions
• On the Levy density function