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On Burdick's symmetry problem

  • Let P be a probability measure of the real line R such that each of the product measures P^{otimes n} assigns the value 1/2 to every half space in R^{n} having the origin as a boundary point. Then P is symmetric.Example: A strictly stable law on R is symmetric iff it has median zero. The treated symmetry problem is related to the problem of characterizing the distribution of X_1 by the distribution of (X_2 + X_1, ... ,X_n + X_1), with X_1, ... ,X_n being independent and identically distributed random variables.

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Author:Lutz Mattner
URN (permanent link):urn:nbn:de:hbz:386-kluedo-4678
Serie (Series number):Report in Wirtschaftsmathematik (WIMA Report) (25)
Document Type:Preprint
Language of publication:English
Year of Completion:1999
Year of Publication:1999
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2000/04/03
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011