集值条件期望的收敛定理

详细信息

Convergence Theorems for Set-valued Conditional Expectations

1. Institute for Information and System Sciences, Faculty of Science, Xi'an Jiaotong University, Xi'an, 710049;
2. Department of Mathematics, Hebei Normal University, Shijiazhuang, 050016

摘要: 本文给出了集合序列弱极限的表示定理,得到了随机集列关于σ-域流的条件期望序列在弱收敛意义下的Fatou型引理和控制收敛定理.
- 集值可测函数 /
- 集值条件期望 /
- 弱极限 /
- Fatou引理
Abstract: In this paper, a representation theorem is given for the weak limit of a sequence of sets in a Banach space. We obtain Fatou’s lemmas and dominated convergence theorems for set-valued conditional expectations with an increasing sequence of σ-fields.
- Measurable multifunction /
- set-valued conditional expectation /
- weak limit /
- Fatou’s lemma