Noncommutative Lebesgue decomposition and contiguity with applications in quantum statistics

被引：4
|
作者：
Fujiwara, Akio [1 ]
Yamagata, Koichi [2 ]
机构：
[1] Osaka Univ, Dept Math, Toyonaka, Osaka 5600043, Japan
[2] Univ Electrocommun, Grad Sch Informat & Engn, Chofu, Tokyo 1828585, Japan
来源：
BERNOULLI | 2020年 / 26卷 / 03期
关键词：
contiguity; Lebesgue decomposition; likelihood ratio; local asymptotic normality; quantum statistics; LOCAL ASYMPTOTIC NORMALITY; THEOREM;
D O I：
10.3150/19-BEJ1185
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：
We herein develop a theory of contiguity in the quantum domain based upon a novel quantum analogue of the Lebesgue decomposition. The theory thus formulated is pertinent to the weak quantum local asymptotic normality introduced in the previous paper [Yamagata, Fujiwara, and Gill, Ann. Statist. 41 (2013) 2197-2217], yielding substantial enlargement of the scope of quantum statistics.
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页码：2105 / 2142
页数：38
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