σ-代数族的局部可比较性与条件期望算子

在多指标鞅和随机过程的研究中,对σ-代数族附加上条件独立性和局部可比较性的条件后,得到了许多满意的结果,本文就局部可比较性在1] 2]的基础上,以希尔伯脱投影算子的观点,研究了条件期望的一些性质,进一步阐述了σ-代数局部可比较性的各种等价命题,以及进一步的性质。

LOCALLY COMPARABLETY OF σ—ALGEBRA VARIETY AND CONDITION EXPECTANCE OPERATOR

The Concept of locally Conparablety of σ—algebra Variety is introducedby Gheorghita Zbayanu and Zhuang Xing Wu(in 1982,It is the mostimportant Concept for study of multiply index martingales and stochasti processes and it helps their numerous basic theorem can hold and ever appr-oach to case of one index,this paper in view of Hilbert space projectionoperator on the fundmentat of1]2]we have studied some propertiesof condition expectance operator,and further,wehave studied equivalentproposition of locally comparablety and more general property。