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arXiv · 1801.01546

Characterization of distributions of $Q$-independent random variables on locally compact Abelian groups

Margaryta Myronyuk
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Abstract

Let $X$ be a second countable locally compact Abelian group. We prove some group analogues of the Skitovich--Darmois, Heyde and Kac--Bernstein characterisation theorems for $Q$-independent random variables taking values in the group $X$. The proofs of these theorems are reduced to solving some functional equations on the character group of the group $X$.

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Margaryta Myronyuk. 2017-12-31. Characterization of distributions of $Q$-independent random variables on locally compact Abelian groups. https://arxiv.org/abs/1801.01546

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