随机算子的期望与不动点  

EXPECTATION AND FIXED POINT OF A RANDOM OPERATOR

作　　者：刘华民[1] 

机构地区：[1]郑州大学数学系

出　　处：《郑州大学学报（自然科学版）》1991年第1期9-11,18,共4页Journal of Zhengzhou University (Natural Science)

摘　　要：令T是一致随机压缩算子,本文证明当T满足下述条件时。T(ω)x=Sx+α(ω),其中 S 是确定性线性压缩算子,α(ω)是 Bochner 可积的随机元,则对于 T,求期望与求不动点的次序可以交换;还以反例说明不满足上述条件时,交换次序所得结果不同。Let T be a uniform random contraction operator.In the paper,it is proved that the expectation of a random fixed point of T coincides with the fixed point of the deterministic operator which arises as the expectation of T when the following condition holds: T(ω)x=Sx+a(ω) where S is a deterministic linear contration operator and a(?)is a Bochner integrable random ele- ment.

关 键 词：随机算子 期望 不动点 

分 类 号：O177.99[理学—数学]