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

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 $X$.

arXiv admin note: substantial text overlap with arXiv:1703.06484

References in corpus (1)

• The Heyde characterization theorem on some locally compact Abelian groups

Cited by in corpus (2)

• On notions of Q-independence and Q-identical distributiveness
• Characterization theorems for Q-independent random variables in Banach spaces