One-sided L\'evy stable distributions
Abstract
In this paper, we show new representations of one-sided L\'evy stable distributions for irrational L\'evy indices of the type (pq)l2l1 which are not covered in pg1 : for rational L\'evy indices. Furthermore, other equivalent representations for a distribution of a rational L\'evy index is described. We also give a simplest proof for the formulae which cover the cases for rational L\'evy indices. Finally we introduce the concepts of L\'evy smashing and L\'evy-smashed gamma stochastic processes.
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