高师理科学刊2025，Vol.45Issue(8)：15-17,3.DOI:10.3969/j.issn.1007-9831.2025.08.003
条件期望平滑性的一个反例
A counterexample of the smoothing property of conditional expectation
左红霞 1陈维2
作者信息
- 1. 伊犁师范大学数学与统计学院,新疆 伊宁 835000
- 2. 伊犁师范大学数学与统计学院,新疆 伊宁 835000||伊犁师范大学应用数学研究所,新疆 伊宁 835000
- 折叠
摘要
Abstract
This paper uses the counterexample construction method to explore how to understand and grasp the smoothing properties of random variable conditional expectations.Inspired by the ideas of Durrett and Stoyanov,the paper constructs and demonstrates a counter-example in which the conditional expected smoothness does not hold in a specific situation.Meanwhile,an example is provided to illustrate the validity of conditional expectation smoothness.The pivotal aspect of the argument lies in the thorough utilization of the measurable properties of random variables based on the σ-fields.关键词
随机变量/条件期望/平滑性Key words
random variable/conditional expectation/smoothing property分类
数理科学引用本文复制引用
左红霞,陈维..条件期望平滑性的一个反例[J].高师理科学刊,2025,45(8):15-17,3.
