B值拟鞅差序列加权和的收敛性与大数律

B值拟鞅差序列加权和的收敛性与大数律 The Convergence and the Law of Large Numbers for Weighted Sums of Quasi-Martingals Difference Series in Banach Spaces 邱德华 QIU De-hua1 1 2 3 first-author 甘师信 GAN Shi-xin2 1 2 3 衡阳师范学院数学系 衡阳师范学院数学系 Department of Mathematics, Hengyang Normal University Department of Mathematics, Hengyang Normal University 武汉大学数学与统计学院,湖南,衡阳,421008 武汉大学数学与统计学院,湖南,衡阳,421008 School of Mathematics and Statistics, Wuhan University School of Mathematics and Statistics, Wuhan University ,湖北,武汉,430072 ,湖北,武汉,430072 {Xn,Fn,n≥1}为B值P拟鞅,{anj}为实值常数阵列,在{}关于{}一致可积的条件下,建立了anjdjX的收敛性与Banach空间p光滑性的关系,并在p光滑Banach空间中,给出anjdjX的强大数定律及完全收敛定理. For weighted sums of the form anjdjX ,Where {anj ,1≤j≤Kn ↑∞}is a real constants ar-ray and{dnX ,n≥1}is quasi-martingale difference series, we establish the relationship between the convergence and the p-smoothable Banach space under the condition of {anj}-uniform integrability,and we get the strong law of large numbers and the complete convergence for weighted sums of quasi-martingale difference series. p光滑Banach空间 一致可积 大数定律 完全收敛 Lp收敛 p-smoothable Banach space uniform integrability law of large numbers complete convergence Lp convergence O211.4;O211.6 国家自然科学基金（10071019,10071058）;湖南省教育厅科研基金（00C262）资助项目 2002-03-01 2021-04-01 3