Stable distributions and harmonic analysis on convex cones

Davydov, Youri; Molchanov, Ilya; Zuyev, Sergei

doi:10.1016/j.crma.2007.01.015

Probability Theory

Stable distributions and harmonic analysis on convex cones

Presented by: Marc Yor

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

Comptes Rendus. Mathématique, Volume 344 (2007) no. 5, pp. 321-326.

Abstract
Résumé

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).

Received: 2006-07-15
Accepted: 2007-01-10
Published online: 2007-02-20

DOI: 10.1016/j.crma.2007.01.015

Author's affiliations:

Davydov, Youri ¹; Molchanov, Ilya ²; Zuyev, Sergei ³

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     title = {Stable distributions and harmonic analysis on convex cones},
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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. https://www.numdam.org/articles/10.1016/j.crma.2007.01.015/

References
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[3] Davydov, Yu.; Molchanov, I.; Zuyev, S. Strictly stable distributions on convex cones, 2006 | arXiv

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[5] Molchanov, I. Theory of Random Sets, Springer, London, 2005

[6] Resnick, S.I. Extreme Values, Regular Variation and Point Processes, Springer, Berlin, 1987

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