条件独立性的三种形式及其相互关系

北京大学学报（自然科学版）

条件独立性的三种形式及其相互关系

李开灿,耿直

北京大学数学学院，北京，100871

收稿日期:2001-12-21 出版日期:2002-09-20 发布日期:2002-09-20

Three Patterns of Conditional Independence and Their Mutual Relationships

LI Kaican，GENG Zhi

School of Mathematics, Peking University, Beijing, 100871

Received:2001-12-21 Online:2002-09-20 Published:2002-09-20

摘要/Abstract

摘要： 给出了随机变量的随机条件独立性、回归条件独立性及其强随机条件独立性的概念，并且证明了这几种条件独立性的相互关系。主要结论是在一定条件下，强随机条件独立必有回归条件独立；随机条件独立性与回归条件独立性是等价的。它们对概率论及其数理统计的应用是有意义的。

关键词: 条件独立, σ-域, 条件期望, 质集

Abstract: Three patterns of the conditional independence are presented, and their mutual relationships among the three conditional independences are proved. The main results include that strong conditional independence can derive regress conditional independence and that regress conditional independence is equivalent to the random conditional independence.

Key words: conditional independence, σ-field, conditional expectation, prime set

中图分类号:

O212.4

李开灿,耿直. 条件独立性的三种形式及其相互关系[J]. 北京大学学报（自然科学版）.

LI Kaican,GENG Zhi. Three Patterns of Conditional Independence and Their Mutual Relationships[J]. Acta Scientiarum Naturalium Universitatis Pekinensis.

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https://xbna.pku.edu.cn/CN/Y2002/V38/I5/629