Abstract : Revisiting an article by Chernin and Ibragimov on unimodality of stable laws, we show that their approach to deduce the general case from the extremal ones, whose completion contained an error as discovered later by Kanter, can be carried out successfully in considering Bochner's subordination and multiplicative strong unimodality. This short proof of the unimodality of all stable densities yields also a multiplicative counterpart to Yamazato's additive ones.
https://hal.univ-lille.fr/hal-02474245
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Soumis le : mardi 11 février 2020 - 11:32:42 Dernière modification le : dimanche 29 novembre 2020 - 03:24:06 Archivage à long terme le : : mardi 12 mai 2020 - 13:32:09
Thomas Simon. A multiplicative short proof for the unimodality of stable densities. Electronic Communications in Probability, 2011, Electronic Communications in Probability, 16, pp.623-629. ⟨10.1214/ecp.v16-1672⟩. ⟨hal-02474245⟩