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A group analog of the Skitovich-Darmois theorem on the group of p-adic numbers Ωp

Le : 17/11/2014 11h00
Par : Gennadyi Feldman (Kharkov)
Lieu :
Lien web :
Résumé : The following statement about characterization of a Gaussian distribution on the real line is one of the most well-known characterization theorems. The Skitovich{Darmois theorem. Let Ej ; j = 1; 2; : : : ; n; n > 2, be independent random variables, j ; j be nonzero real numbers. If the linear forms L1 = 1+ ... + n n and L2 = 1 + ... + nn are independent, then all j are Gaussian. We discuss a generalization of this theorem in the case, when independent ran- dom variables take values in the group of p-adic numbers Ωp and coefficients of the considering linear forms are topological automorphisms of Ωp. All necessary concepts concerning the group of p-adic numbers Ωp will be given in the rst part of the talk.