On a functional equation generalizing the class of semistable distributions |
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Authors: | Mohamed Ben Alaya Thierry Huillet |
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Affiliation: | (1) LAGA, CNRS (UMR 7539), Institut Galilée, Université de Paris 13, 93430 Villetaneuse, France;(2) LPTM, Université de Cergy-Pontoise et CNRS (UMR 8089), 5, mail Gay-Lussac, Neuville sur Oise, 95031 Cergy-Pontoise Cedex, France |
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Abstract: | With ?(p),p≥0 the Laplace-Stieltjes transform of some infinitely divisible probability distribution, we consider the solutions to the functional equation ?(p-e ?pβΠ i=1 m ?γi (c i p) for somem≥1,c i>0, γ i >0,i=1., …,m, β ε ®. We supply its complete solutions in terms of semistable distributions (the ones obtained whenm=1). We then show how to obtain these solutions as limit laws (r → ∞) of normalized Poisson sums of iid samples when the Poisson intensity λ(r) grows geometrically withr. |
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Keywords: | KeywordHeading" > and phrases Stable and semistable laws functional equation limit laws selfsimilarity generalized semistability |
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