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Issue ESAIM: PS
Volume 7, 2003
Page(s) 313 - 328
DOI 10.1051/ps:2003014

ESAIM: P&S, May 2003, Vol. 7, pp. 313-328
DOI: 10.1051/ps:2003014

Constraints on distributions imposed by properties of linear forms

Denis Belomestny

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


(Received April 22, 2002. Revised March 17, 2003.)

Abstract
Let $(X_1,Y_1),\ldots,(X_m,Y_m)$ be m independent identically distributed bivariate vectors and $L_1=\beta_1X_1+\ldots+\beta_mX_m$, $L_2=\beta_1Y_1+\ldots+\beta_mY_m$ are two linear forms with positive coefficients. We study two problems: under what conditions does the equidistribution of L1 and L2 imply the same property for X1 and Y1, and under what conditions does the independence of L1 and L2 entail independence of X1 and Y1? Some analytical sufficient conditions are obtained and it is shown that in general they can not be weakened.


Mathematics Subject Classification. 62E10, 60E10.

Key words: Equidistribution, independence, linear forms, characteristic functions.


© EDP Sciences, SMAI 2003


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