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Short Communications

Independent random variables on Abelian groups with independent sum and difference

G. M. Feldman

B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, Khar'kov

Abstract: Let $X$ be a second countable locally compact Abelian group. Let $\xi_1$, $\xi_2$ be independent random variables with values in the group $X$ and distributions $\mu_1$, $\mu_2$ such that the sum $\xi_1+\xi_2$ and the difference $\xi_1-\xi_2$ are independent. Assuming that the connected component of the zero of group $X$ contains a finite number of elements of order 2, we describe the possible distributions $\mu_k$.

Received: 23.09.2014
Revised: 08.09.2015

DOI: 10.4213/tvp5064

 English version: Theory of Probability and its Applications, 2017, 61:2, 335–345

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