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arXiv · 1510.04798

Independent random variables on Abelian groups with independent the sum and difference

G. M. Feldman
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Abstract

Let X be a second countable locally compact Abelian group. Let $ξ_1, ξ_2$ be independent random variables with values in the group X and distributions $μ_1, μ_2$ such that the sum $ξ_1+ξ_2$ and the difference $ξ_1-ξ_2$ are independent. Assuming that the connected component of zero of the group $X$ contains a finite number elements of order 2 we describe the possible distributions $μ_k$.

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G. M. Feldman. 2015-10-16. Independent random variables on Abelian groups with independent the sum and difference. https://arxiv.org/abs/1510.04798

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