E值鞅型序列在条件期望下的收敛性与E值鞅的局部收敛性

ON CONVERGENCE OF CONDITIONAL EXPECTATIONS OF BANACH VALUED MARTINGALE-LIKE SEQUENCES AND LOCAL CONVERGENCE OF BANACH VALUED MARTINGALES

本文讨论了 E 值随机变量序列的条件一致可积性,得到了条件一致可积性的几个等价条件,由此知:M.M.Rao 对实值随机变量序列给出的关于σ代数 B 条件一致可积性的定义与 W.Zieba 给出的定义是等价的。另外,我们考察了 E 值鞅型序到在条件期望下的收敛性与 E 值鞅的局部收敛性,得到了一些新结论,同时推广与改进了一些已知的结果。

In this paper we discuss conditionally uniform integrability of a Banach valued random variable sequence relative to a σ-algebra BF.Some equivalent conditions are obtained.It follows that the definitions of conditionally uniform integrability of a real valued random variable sequence with respect to B given by M.M.Rao[4]and W.Zieba[6]are equivalent.In other direction we investigate convergence of conditional expectations of Banaeh valued martingale -like sequences and local convergence of Banaeh valued martingales.Some new results are achieved and some known results are improved.