Abstract Let x = （xn）n≥1 be a martingale on a noncommutative probability space （М,τ） and （Wn）n≥1 a sequence of positive numbers such that Wn =∑^n_k=1 wk→∞ as n→∞. We prove that x = （Xn）n≥1 converges...Abstract Let x = （xn）n≥1 be a martingale on a noncommutative probability space （М,τ） and （Wn）n≥1 a sequence of positive numbers such that Wn =∑^n_k=1 wk→∞ as n→∞. We prove that x = （Xn）n≥1 converges bilaterally almost uniformly （b.a.u.） if and only if the weighted average （σan（x））n≥1 of x converges b.a.u, to the same limit under some condition, where σn（x） is given by σn（x）=1/Wn ^n∑_k=1 wkxk,n=1,2,… Furthermore, we prove that x = （xn）n≥1 converges in Lp（М） if and only if （σ＇n（x））n≥1 converges in Lp（М）, where 1 ≤p 〈 ∞ .We also get a criterion of uniform integrability for a family in L1（М）.展开更多
利用负超可加相依(NSD)随机阵列的Rosenthal型矩不等式和截尾方法,在随机阵列{X nk,1≤k≤k n,n≥1}关于{a nk,1≤k≤k n,n≥1}一致可积的条件下,讨论NSD随机阵列加权和最大值max 1≤j≤k n∑j k=1 a nk X nk-E∑j k=1 a nk X nk的弱收...利用负超可加相依(NSD)随机阵列的Rosenthal型矩不等式和截尾方法,在随机阵列{X nk,1≤k≤k n,n≥1}关于{a nk,1≤k≤k n,n≥1}一致可积的条件下,讨论NSD随机阵列加权和最大值max 1≤j≤k n∑j k=1 a nk X nk-E∑j k=1 a nk X nk的弱收敛、L r收敛和完全收敛性.展开更多
基金supported by National Natural Science Foundation of China (Grant No.11071190)
文摘Abstract Let x = （xn）n≥1 be a martingale on a noncommutative probability space （М,τ） and （Wn）n≥1 a sequence of positive numbers such that Wn =∑^n_k=1 wk→∞ as n→∞. We prove that x = （Xn）n≥1 converges bilaterally almost uniformly （b.a.u.） if and only if the weighted average （σan（x））n≥1 of x converges b.a.u, to the same limit under some condition, where σn（x） is given by σn（x）=1/Wn ^n∑_k=1 wkxk,n=1,2,… Furthermore, we prove that x = （xn）n≥1 converges in Lp（М） if and only if （σ＇n（x））n≥1 converges in Lp（М）, where 1 ≤p 〈 ∞ .We also get a criterion of uniform integrability for a family in L1（М）.
文摘利用负超可加相依(NSD)随机阵列的Rosenthal型矩不等式和截尾方法,在随机阵列{X nk,1≤k≤k n,n≥1}关于{a nk,1≤k≤k n,n≥1}一致可积的条件下,讨论NSD随机阵列加权和最大值max 1≤j≤k n∑j k=1 a nk X nk-E∑j k=1 a nk X nk的弱收敛、L r收敛和完全收敛性.
