INDEPENDENT LINEAR STATISTICS ON a-ADIC SOLENOIDS

被引：7
作者：
Feldman, G. M. [1 ]
机构：
[1] Inst Low Temp Phys & Engn, UA-61103 Kharkov, Ukraine
来源：
THEORY OF PROBABILITY AND ITS APPLICATIONS | 2010年 / 54卷 / 03期
关键词：
independent linear statistics; a-adic solenoid; topological automorphism; SKITOVICH-DARMOIS THEOREM; ABELIAN-GROUPS; GAUSSIAN DISTRIBUTIONS; VARIABLES;
D O I：
10.1137/S0040585X97984322
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
Let xi(1) and xi(2) be independent random variables with values in an a-adic solenoid Sigma(a) and distributions mu(1), mu(2). Let alpha(j), beta(j) be topological automorphisms of the group Sigma(a). Assuming that the linear statistics L-1 = alpha(1)xi(1) + alpha(2)xi(2) and L-2 = beta(1)xi(1) + beta(2)xi(2) are independent, we describe possible distributions mu(1) and mu(2).
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页码：375 / 388
页数：14
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