Probability Theory
Stable distributions and harmonic analysis on convex cones
Comptes Rendus. Mathématique, Volume 344 (2007) no. 5, pp. 321-326.

We consider α-stable random elements in a general convex cone K and show how their main properties: sign and range of α, LePage representation and Lévy decomposition are related to the algebraic and metric properties of K: distributivity laws, coincidence of the origin and the neutral elements, existence of a homogeneous norm, and separating family of semi-continuous characters.

On considère les éléments aléatoires α-stables à valeurs dans un cône convexe abstrait K. On montre que les propriétés principales de stabilité (telles que : le signe et l'intervalle du paramètre α, la représentation de LePage et la décomposition de Lévy) sont étroitement liées aux propriétés algébriques et métriques de K (telles que : les lois de distributivité, coïncidence de l'origine et de l'élément neutre, l'existence de la norme homogène et d'une famille de caractères semi-continus).

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Published online:
DOI: 10.1016/j.crma.2007.01.015
Davydov, Youri 1; Molchanov, Ilya 2; Zuyev, Sergei 3

1 Laboratoire Paul-Painlevé, Université Lille 1, UFR de mathématiques, 59655 Villeneuve d'Ascq cedex, France
2 Department of Mathematical Statistics and Actuarial Science, University of Berne, Sidlerstr. 5, CH-3012 Berne, Switzerland
3 Department of Statistics and Modelling Science, University of Strathclyde, Glasgow G1 1XH, UK
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Davydov, Youri; Molchanov, Ilya; Zuyev, Sergei. Stable distributions and harmonic analysis on convex cones. Comptes Rendus. Mathématique, Volume 344 (2007) no. 5, pp. 321-326. doi : 10.1016/j.crma.2007.01.015. http://www.numdam.org/articles/10.1016/j.crma.2007.01.015/

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