Independence of linear forms with random coefficients

• 成果类型: Article
• 署名作者: Chistyakov, G. P.; Goetze, F.
• 署名单位: National Academy of Sciences Ukraine; B. Verkin Institute for Low Temperature Physics & Engineering of the National Academy of Sciences of Ukraine; University of Bielefeld
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-006-0503-6
• 发表日期: 2007
• 页码: 1-24
• 关键词: dependent random-variables; darmois-skitovitch; THEOREM

摘要

We extend the classical Darmois-Skitovich theorem to the case where the linear forms L-r1 = U1X1 +center dot center dot center dot+ UnXn and L-r2 = Un+1X1+center dot center dot center dot+U2nXn have random coefficients U-1,...,U-2n. Under minimal restrictions on the random coefficients we completely describe the distributions of the independent random variables X-1,...,X-n and U-1,...,U-2n such that the linear forms L-r1 and L-r2 are independent.