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- W1970553685 abstract "It is well known that the independence of two linear forms with nonzero coefficients of independent random variables implies that the random variables are Gaussian (the Skitovich-Darmois theorem). The analogous result holds true for two linear forms of independent random vectors with nonsingular matrices as coefficients (the Ghurye-Olkin theorem). In this paper we give the complete description of locally compact Abelian groups X for which the independence of two linear forms of independent random variables with values in X having distributions with nonvanishing characteristic functions (coefficients of the forms are topological automorphisms of X) implies that the random variables are Gaussian." @default.
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- W1970553685 date "2003-05-01" @default.
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- W1970553685 title "A characterization of the Gaussian distribution on Abelian groups" @default.
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- W1970553685 doi "https://doi.org/10.1007/s00440-003-0256-4" @default.
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