摘要
讨论了Ｂ值随机变量阵列加权和的Ｌｒ收敛性与弱大数律．证明了取值于可分Ｐ型空间的行独立的随机变量阵列加权和在一定的条件下具有Ｌｒ收敛性，从而更有弱大数律成立．本文的结果推广与改进了若干重要经典的弱大数定理．同时，用独立的Ｃｅｓａｒｏ一致可积的Ｂ值随机变量序列加权和的Ｌｒ收敛性刻划了ｐ型空间．
Lr convergence and the weak laws of large numbers for weighted sums of arrays of Banach valued random variables are discussed in this paper. The following result is proved:Let B be a seperable Banach space of type p (1 <p《2). {Xm, 1《i〈kn↑》1 } is an array of rowwise independent Banach valued random variables. {am ,1《i〈kn,n》1} is an array of real numbers. 1《r<p. If the following conditions are satisfied: is Cesdro uniformly integrable,k(2) 1, where C is positive constant,thenIn the other direction, Banach space of p-type is characterized by L' convergence of weighted sums of sequences of Cesdro uniformly integrable Banach valued random variables.
出处
《武汉大学学报（自然科学版）》
CSCD
1995年第5期533-540,共8页
Journal of Wuhan University(Natural Science Edition)
基金
国家自然科学基金
国家教委博士学科点专项基金
关键词
随机变量阵列
加权和
L^R收敛性
弱大数律
p-type space
Cesaro uniform integrability
weighted sums of arrays of random variables
L￣r convergence
weak law of large numbers
