This article is cited in 22 papers

Short Communications

More on the Skitovich–Darmous theorem for finite Abelian groups

G. M. Feldman

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

Abstract: The following theorem is proved. Let $X$ be a finite Abelian group and $\xi_1, \xi_2$ be independent random variables with values in $X$ and with distributions $\mu_1, \mu_2$. Then the independence of the linear statistics $L_1=\alpha_1(\xi_1) + \alpha_2(\xi_2)$ and $L_2=\beta_1(\xi_1) + \beta_2(\xi_2)$, where $\alpha_j, \beta_j$ are automorphisms of the group $X$, implies that $\mu_1,\mu_2$ are idempotent distributions.

Keywords: characterization of probability distributions, independence of linear statistics, finite Abelian group.

Received: 01.12.1998

DOI: 10.4213/tvp490

 English version: Theory of Probability and its Applications, 2001, 45:3, 507–511

Bibliographic databases:

• 
• 
•