Characterization theorems for $Q$-independent random variables with values in a locally compact Abelian group
Probability
2017-03-21 v1
Abstract
Let be a locally compact Abelian group, be its character group. Following A. Kagan and G. Sz\'ekely we introduce a notion of -independence for random variables with values in . We prove group analogues of the Cram\'er, Kac-Bernstein, Skitovich-Darmois and Heyde theorems for -independent random variables with values in . The proofs of these theorems are reduced to solving some functional equations on the group .
Keywords
Cite
@article{arxiv.1703.06484,
title = {Characterization theorems for $Q$-independent random variables with values in a locally compact Abelian group},
author = {Gennadiy Feldman},
journal= {arXiv preprint arXiv:1703.06484},
year = {2017}
}