Constraints on distributions imposed by properties of linear forms
ESAIM: Probability and Statistics, Tome 7 (2003), pp. 313-328

Let (X 1 ,Y 1 ),...,(X m ,Y m ) be m independent identically distributed bivariate vectors and L 1 =β 1 X 1 +...+β m X m , L 2 =β 1 Y 1 +...+β m Y m are two linear forms with positive coefficients. We study two problems: under what conditions does the equidistribution of L 1 and L 2 imply the same property for X 1 and Y 1 , and under what conditions does the independence of L 1 and L 2 entail independence of X 1 and Y 1 ? Some analytical sufficient conditions are obtained and it is shown that in general they can not be weakened.

DOI : 10.1051/ps:2003014
Classification : 62E10, 60E10
Keywords: equidistribution, independence, linear forms, characteristic functions 
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     author = {Belomestny, Denis},
     title = {Constraints on distributions imposed by properties of linear forms},
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     year = {2003},
     publisher = {EDP Sciences},
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     doi = {10.1051/ps:2003014},
     mrnumber = {1987791},
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     url = {https://www.numdam.org/articles/10.1051/ps:2003014/}
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Belomestny, Denis. Constraints on distributions imposed by properties of linear forms. ESAIM: Probability and Statistics, Tome 7 (2003), pp. 313-328. doi: 10.1051/ps:2003014

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