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Characterization theorems for $Q$-independent random variables with values in a locally compact Abelian group by Feldman, Gennadiy is a scholarly article available to read on EtoBox.

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

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 $Y$.

Author

Feldman, Gennadiy

Published

2017

Language

EN