Constraints on distributions imposed by properties of linear forms

Belomestny, Denis

doi:10.1051/ps:2003014

Belomestny, Denis

ESAIM: Probability and Statistics, Tome 7 (2003), pp. 313-328.

Résumé

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.

MR Zbl

DOI : 10.1051/ps:2003014

Classification : 62E10, 60E10
Mots-clés : 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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     pages = {313--328},
     publisher = {EDP-Sciences},
     volume = {7},
     year = {2003},
     doi = {10.1051/ps:2003014},
     mrnumber = {1987791},
     zbl = {1013.62059},
     language = {en},
     url = {https://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. https://numdam.org/articles/10.1051/ps:2003014/

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