摘要
设B是一实可分的Banach空间,具有Radon-Nikodyn性质(RNP).{Xn,n≥1}是L1B中的序列,其子序列{Xs,s∈S}是一L1极限鞅.证明了{Xn,n≥1}是L1S-game的充分必要条件是{Xn,n≥1}在条件liminfnE‖XSn‖<∞下或条件∫{τ<∞}‖XSτ‖dP<∞,τ∈下依概率收敛,其中是由{Fn,n∈N}的停时组成的集合,Sn=inf{s∈S:n≤s},n∈N.这个结论推广与改进了Luu的相关结果.而行独立的B值随机变量阵列完全收敛性的两个结果则改进与推广了T.C.Hu等人的相应结果.
Let B be a real separable Banach space with the RNP and {Xn,n≥1} a sequence in LB^1 such that its subsequence {Xs,s∈ S} is an L^1-amart. We prove that {Xn,n≥1} is an L^1S-game iff it converges in probability under the condition liminfE‖XSτ‖〈∞ or ∫（τ〈∞）‖XSτ‖dP〈∞,A↓τ∈^-T where ^-T is the set of all stopping times with respect to {Fn,n∈N} and Sn=inf{s∈S：n≤s},n∈N, n E N. This result extends and improves the corresponding results of Luu. The results of complete canvergence for arrays of random variables extend and improve the corresponding results of Hu et al.
出处
《武汉大学学报（理学版）》
CAS
CSCD
北大核心
2007年第1期29-32,共4页
Journal of Wuhan University:Natural Science Edition
基金
国家自然科学基金资助项目(10671149)
