摘要
在实可分的Banach空间上有一类特殊的空间———α(α≤2)阶光滑空间,利用单调函数的性质、截尾法以及Doob鞅收敛定理,讨论了取值于α阶光滑空间的可积随机变量序列的强极限定理.作为推论,得到关于鞅差序列的极限定理,最后利用单调函数的性质及截尾法得到取值于实可分的Banach空间的可积随机变量的极限定理.
α （α≤2）-th smooth space is a special space in the real seperable Banach space. In this paper, the strong limit theorems about series of integrable random variables which are in the a-th smooth space are obtained firstly by using properties of monotone functions, the truncation method and Doob martingale convergence theorem, As a conclusion, the limit theorems about series of random variables of martingale difference are obtained. Finally the strong limit theorem about series of integrable random variables which are in the real seperable Banach space is obtained with the properties of monotone functions and the truncation method.
出处
《天津师范大学学报（自然科学版）》
CAS
2006年第4期51-53,共3页
Journal of Tianjin Normal University：Natural Science Edition
基金
河北省博士基金资助项目(535007)
