The Lukacs-Olkin-Rubin Theorem on Symmetric Cones Without Invariance of the "Quotient"

作     者：Kolodziejek, Bartosz 

作者机构：Warsaw Univ Technol Fac Math & Informat Sci Pl Politech 1 PL-00661 Warsaw Poland 

出 版 物：《JOURNAL OF THEORETICAL PROBABILITY》 (理论概率杂志)

年 卷 期：2016年第29卷第2期

页      面：550-568页

核心收录：

学科分类：07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：NCN [2012/05/B/ST1/00554] 

主　　题：Lukacs characterization Division algorithm Wishart distribution Riesz distribution Symmetric cones Functional equations 

摘      要：We prove the Lukacs-Olkin-Rubin theorem without invariance of the distribution of the quotient, which was the key assumption in the original proof of (Olkin-Rubin in Ann Math Stat 33:1272-1280, 1962). Instead, we assume existence of strictly positive continuous densities of respective random variables. We consider the (cone variate) quotient for any division algorithm satisfying some natural conditions. For that purpose, a new proof of the Olkin-Baker functional equation on symmetric cones is given.