B值随机变量阵列加权和的L^r收敛性与弱大数律

B值随机变量阵列加权和的L r 收敛性与弱大数律 L￣r CONVERGENCE AND WEAK LAWS OF LARGE NUMBERS FOR WEIGHTED SUMS OF ARRAYS OF BANACH VALUED RANDOM VARIABLES 甘师信 Gan Shixin 1 first-author 武汉大学数学系 武汉大学数学系 Department of Mathematics,Wuhan University Department of Mathematics,Wuhan University 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. p型空间 Cesaro一致可积性 随机变量阵列加权和 Lr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 O211.5 国家自然科学基金,国家教委博士学科点专项基金 1995-05-01 2021-04-01 5