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

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Abstract

Let X be a locally compact Abelian group, Y be its character group. Following A. Kagan and G. Székely we introduce a notion of Q-independence for random variables with values in X. We prove group analogues of the Cramér, 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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  1. B. Verkin Institute for Low Temperature Physics and Engineering, Kharkiv, Ukraine

    Gennadiy Feldman

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  1. Gennadiy Feldman
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Correspondence to Gennadiy Feldman.

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Feldman, G. Characterization theorems for Q-independent random variables with values in a locally compact Abelian group. Aequat. Math. 91, 949–967 (2017). https://doi.org/10.1007/s00010-017-0479-6

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  • DOI: https://doi.org/10.1007/s00010-017-0479-6

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