ON ALMOST SURE CONVERGENCE OF WEIGHTED SUMS OF RANDOM ELEMENT SEQUENCES  

作　　者：甘师信 

机构地区：[1]School of Mathematics and Statistics, Wuhan University

出　　处：《Acta Mathematica Scientia》2010年第4期1021-1028,共8页数学物理学报（B辑英文版）

基　　金：Supported by the National Natural Science Foundationof China (10671149)

摘　　要：We mainly study the almost sure limiting behavior of weighted sums of the form ∑ni=1 aiXi/bn , where {Xn, n ≥ 1} is an arbitrary Banach space valued random element sequence or Banach space valued martingale difference sequence and {an, n ≥ 1} and {bn,n ≥ 1} are two sequences of positive constants. Some new strong laws of large numbers for such weighted sums are proved under mild conditions.We mainly study the almost sure limiting behavior of weighted sums of the form ∑ni=1 aiXi/bn , where {Xn, n ≥ 1} is an arbitrary Banach space valued random element sequence or Banach space valued martingale difference sequence and {an, n ≥ 1} and {bn,n ≥ 1} are two sequences of positive constants. Some new strong laws of large numbers for such weighted sums are proved under mild conditions.

关 键 词：Strong law of large number almost sure convergence Lp convergence weighted sums Banach space valued random element sequence Banach space martingale difference sequence 

分 类 号：O177.2[理学—数学]