B值鞅差阵列加权和的L^r收敛性与弱大数定律

B值鞅差阵列加权和的L r 收敛性与弱大数定律 L￣r CONVERGENCE OF WEIGHTED SUMS OF BANACH SPACE VALUED MARTINGALE DIFFERENCE ARRAYS AND THE WEAK LAW OF LARGE NUMBERS 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 给出了Ｂ值鞅差阵列加权和在Ｃｅｓａｒｏ一致可积性假设条件下成立的一些极限定理，本文的讨论说明Ｃｅａｒｏ一致可积性在研究加权和的极限定理时是一个很有效的工具，结论推广与改进了若干熟知的重要结果． in this paper we discuss Lr convergence of weiShted sums of martingale difference arrays with values in Banach space and the weak law of large numbers under the condition of uniform integrability in the Cesaro sence. Some general results are obtained in this aspect. Our discussion shows that the Cesaro uniform integrability is an effective and useful tool in the study of limit theorems ofweighted sums of martingale difference arrays. B值鞅差阵列 p阶可光滑空间 Cedro一致可积性 lp－Toeplitz矩阵 Lr收敛性 弱大数定律 martingale difference array with values in Banach space p-smoothable space uniform integrability in the Cesaro since lp-Toeplitz mains L￣r convergence weak law of large numbers O212 国家自然科学基金,国家教委博士学科点专项基金 1994-01-01 2021-04-01 1