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

Margaryta Myronyuk

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

Probability 2018-01-08 v1

Authors: Margaryta Myronyuk

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 $X$ .

Keywords

locally compact abelian groups q-independent random variables characterisation theorems functional equations character group

Cite

@article{arxiv.1801.01546,
  title  = {Characterization of distributions of $Q$-independent random variables on locally compact Abelian groups},
  author = {Margaryta Myronyuk},
  journal= {arXiv preprint arXiv:1801.01546},
  year   = {2018}
}

Comments

arXiv admin note: substantial text overlap with arXiv:1703.06484

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