Abstract:
A new representation is proposed for the scale factor (so-called standard) in the Eaton problem on n-dimensional versions of random vectors. An extension of the Eaton problem to the nonsymmetric case is formulated. A new approach based on analysis of multiplicative properties of random vectors and random variables is suggested, which permits, in particular, to establish, with uniformity of attitude, most of the presently known results on description of classes of n-dimensional versions.
Keywords:
standard, Eaton, the Eaton problem, n-dimensionalversion, multiplicative properties, distribution.
Citation:
A. D. Lisitskii, “The Eaton problem and multiplicative properties of multivariate distributions”, Teor. Veroyatnost. i Primenen., 42:4 (1997), 696–714; Theory Probab. Appl., 42:4 (1998), 618–632
\Bibitem{Lis97}
\by A.~D.~Lisitskii
\paper The Eaton problem and multiplicative properties of~multivariate distributions
\jour Teor. Veroyatnost. i Primenen.
\yr 1997
\vol 42
\issue 4
\pages 696--714
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\crossref{https://doi.org/10.4213/tvp2180}
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\zmath{https://zbmath.org/?q=an:0921.62067}
\transl
\jour Theory Probab. Appl.
\yr 1998
\vol 42
\issue 4
\pages 618--632
\crossref{https://doi.org/10.1137/S0040585X97976453}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000079809500006}
Linking options:
https://www.mathnet.ru/eng/tvp2180
https://doi.org/10.4213/tvp2180
https://www.mathnet.ru/eng/tvp/v42/i4/p696
This publication is cited in the following 4 articles:
J.K. Misiewicz, Z. Volkovich, “Every symmetric weakly-stable random vector is pseudo-isotropic”, Journal of Mathematical Analysis and Applications, 483:1 (2020), 123575
V. P. Zastavnyi, A. D. Manov, “On the Positive Definiteness of Some Functions Related to the Schoenberg Problem”, Math. Notes, 102:3 (2017), 325–337
Nils Chr. Framstad, “Portfolio Theory forα-Symmetric and Pseudoisotropic Distributions:k-Fund Separation and the CAPM”, Journal of Probability and Statistics, 2015 (2015), 1
Alexander Koldobsky, “Positive definite functions and stable random vectors”, Isr. J. Math., 185:1 (2011), 277
Citation in format AMSBIB
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