A characterization of self-decomposable probabilities on the half-line

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1979 English Publisher:Springer Science and Business Media LLCJournal:Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, volume 49, pages 349-352 (issn: 0044-3719, eissn: 1432-2064,

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Authors: Forst, Gunnar;

doi: 10.1007/bf00535505

A characterization of self-decomposable probabilities on the half-line

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Abstract

It is shown that a probability measure μ on ℝ+ is self-decomposable if and only if for s>0 the sequence $$\left( {\frac{1}{{n!}}\mathop \smallint \limits_0^\infty e^{ - ts} (ts)^n d\mu (t)} \right)_{n \geqq 0} ,$$ determines a probability on ℕ0, that is self-decomposable in the sense of Steutel and van Harn.

Keywords

characterization of self-decomposable probabilities, Infinitely divisible distributions; stable distributions

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