摘要
目的讨论了L2(Ω,F,P)空间上投影映射与条件数学期望的等价性。方法采用了逻辑推理的方法进行了证明。结果证明了L2(Ω,F,P)空间上的投影映射就是条件数学期望E(ξ|R)。结论表明在L2(Ω,F,P)空间上,条件数学期望E(ξ|R)是唯一满足投影方程的投影映射。
Aim The equivalence of the projection mapping and the conditional expectation in L^2(Ω,F,P) space are investigated. Methods The equivalence is proved with logical inference meth- od. Results It is proved that the projection mapping in L^2(Ω,F,P) space is conditional expectation E(ξ|R). Conclusion The results show that the conditional expectation is the only projection mapping that meets the projection equation.
出处
《宝鸡文理学院学报(自然科学版)》
CAS
2009年第1期19-21,共3页
Journal of Baoji University of Arts and Sciences(Natural Science Edition)
基金
宝鸡文理学院科研基金资助项目(zk0695)
关键词
投影定理
投影方程
条件数学期望
projection theorem
projection equation
conditional expectation