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Article Dans Une Revue Journal of the Australian Mathematical Society Année : 2010

The Skitovitch-Darmois theorem for locally compact Abelian groups

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Gennadiy Feldman
  • Fonction : Auteur

Résumé

According to the Skitovich–Darmois theorem, the independence of two linear forms of n independent random variables implies that the random variables are Gaussian. We consider the case where independent random variables take values in a second countable locally compact abelian group X, and coefficients of the forms are topological automorphisms of X. We describe a wide class of groups X for which a group-theoretic analogue of the Skitovich–Darmois theorem holds true when n=2.

Dates et versions

hal-03031606 , version 1 (30-11-2020)

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Gennadiy Feldman, Piotr Graczyk. The Skitovitch-Darmois theorem for locally compact Abelian groups. Journal of the Australian Mathematical Society, 2010, 88 (03), pp.339 - 352. ⟨10.1017/S1446788710000224⟩. ⟨hal-03031606⟩
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