B值鞅差序列加权和的收敛性与大数定律

B值鞅差序列加权和的收敛性与大数定律 The Convergence and the Law of Large Numbers for Weghted Sums of Martingale Difference Series in Banach Spaces 甘师信 GAN Shi\|xin 1 first-author 张峰 ZHANG Feng 1 叶臣 YE Chen 1 武汉大学数学与计算机科学学院,武汉,430072 武汉大学数学与计算机科学学院,武汉,430072 College of Mathematics and Computer Science, Wuhan University College of Mathematics and Computer Science, Wuhan University 对形如 knj=1anjdj X的加权和 ,其中 { dn X ,n≥ 1}为 B值鞅差序列 ,{ anj}为实值常数阵列 ,在{‖ dj X‖ p关于 { | anj| p }一致可积的条件下建立鞅差序列加权和的收敛性与 Banach空间 p光滑性的关系 ,并给出p光滑 Banach空间中鞅差序列加权和的强大数定律 For weighted sums of the form k nj=1a nj d jX,where{a nj ,1≤j≤k n↑∞} is a real constants array and {d nX,n≥1} is martingale difference series,we establish the relationship between the convergence and the p\|smoothable Banach space under the condition of {a nj }\|uniform integrability,andwe get the strong law of large numbers for weighted sums of martigale difference series. 鞅差序列加权和 p光滑Banach空间 {Xn,n≥1}关于{ anj }一致可积 强大数定律 弱大数定律 Lp收敛 10.14188/j.1671-8836.2000.03.002 O211 国家自然科学基金!（19610 66）;国家博士学科点专项基金!（9548613）资助项目 2000-03-01 2021-04-01 3