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arXiv · 1703.06484

Characterization theorems for $Q$-independent random variables with values in a locally compact Abelian group

Gennadiy Feldman
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Abstract

Let $X$ be a locally compact Abelian group, $Y$ be its character group. Following A. Kagan and G. Sz\'ekely we introduce a notion of $Q$-independence for random variables with values in $X$. We prove group analogues of the Cram\'er, Kac-Bernstein, Skitovich-Darmois and Heyde theorems for $Q$-independent random variables with values in $X$. The proofs of these theorems are reduced to solving some functional equations on the group $Y$.

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Gennadiy Feldman. 2017-03-19. Characterization theorems for $Q$-independent random variables with values in a locally compact Abelian group. https://arxiv.org/abs/1703.06484

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