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Constraints on distributions imposedby properties of linear forms

Published online by Cambridge University Press:  15 May 2003

Denis Belomestny
Denis Belomestny*
Affiliation:
Institute fur Angewandte Mathematik, Universität Bonn, Interdisziplinares Zentrum für Komplexe Systeme, Meckenheimer Allee 176, 53115 Bonn, Germany; db@izks.uni-bonn.de.
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Abstract

Let (X1,Y1),...,(Xm,Ym ) be m independent identicallydistributed bivariate vectorsandL1 = β1X1 + ... + βmXm , L2 = β1X1 + ... + βmXm are two linear forms with positive coefficients.We study two problems:under what conditions does the equidistribution of L 1 and L 2imply the same property forX 1 and Y 1, and under what conditions does the independence of L 1and L 2 entail independenceof X 1 and Y 1?Some analytical sufficient conditions are obtained and it is shownthat in general they can not be weakened.

Keywords

Equidistributionindependencelinearformscharacteristic functions.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 7 , March 2003 , pp. 313 - 328
Copyright
© EDP Sciences, SMAI, 2003

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References

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