Independent linear forms on connected Abelian groups

✍ Scribed by Gennadiy Feldman; Margaryta Myronyuk

• Publisher: John Wiley and Sons
• Year: 2011
• Tongue: English
• Weight: 149 KB
• Volume: 284
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200810101

✦ Synopsis

Abstract

According to the classical Skitovich‐Darmois theorem the independence of two linear forms of independent random variables implies that the random variables are Gaussian. We prove an analog of this theorem for some locally compact Abelian groups. It turns out that in the considered case the random variables are either Gaussian or their distributions are convolutions of Gaussian distributions and some signed measures. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim