Let (xn,(?)n) be a uniform amart. If sap E||xn||=∞, then there exists a stopping time τsuch that E||xτ||I(τ【∞)=∞. Moreover, if E has RNP, then every vector-valued mil (GFT) of class (C) converges a. s. (in prob...Let (xn,(?)n) be a uniform amart. If sap E||xn||=∞, then there exists a stopping time τsuch that E||xτ||I(τ【∞)=∞. Moreover, if E has RNP, then every vector-valued mil (GFT) of class (C) converges a. s. (in probability) strongly.展开更多
The concepts of conditional expectations, martingales and stopping times were extended to the Riesz space context by Kuo, Labuschagne and Watson (Discrete time stochastic processes on Riesz spaces, Indag. Math.,15(2...The concepts of conditional expectations, martingales and stopping times were extended to the Riesz space context by Kuo, Labuschagne and Watson (Discrete time stochastic processes on Riesz spaces, Indag. Math.,15(2004), 435-451). Here we extend the definition of an asymptotic martingale (amart) to the Riesz spaces context, and prove that Riesz space amarts can be decomposed into the sum of a martingale and an adapted sequence convergent to zero. Consequently an amart convergence theorem is deduced.展开更多
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...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。展开更多
基金Project supported by the National Natural Science Foundation of China
文摘Let (xn,(?)n) be a uniform amart. If sap E||xn||=∞, then there exists a stopping time τsuch that E||xτ||I(τ【∞)=∞. Moreover, if E has RNP, then every vector-valued mil (GFT) of class (C) converges a. s. (in probability) strongly.
基金the John Knopfmacher Centre for Applicable Analysis and Number Theory
文摘The concepts of conditional expectations, martingales and stopping times were extended to the Riesz space context by Kuo, Labuschagne and Watson (Discrete time stochastic processes on Riesz spaces, Indag. Math.,15(2004), 435-451). Here we extend the definition of an asymptotic martingale (amart) to the Riesz spaces context, and prove that Riesz space amarts can be decomposed into the sum of a martingale and an adapted sequence convergent to zero. Consequently an amart convergence theorem is deduced.
文摘本文讨论了 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。