B值一致渐近鞅极限定理的一个注记

A Note on the Limit Theorems for Banach Space Values Uniform Amart

设B是 p阶一致光滑的Banach空间 ,1 p 2 ,X =(Xn,Fn,n 1)是B值一致渐近鞅 ,则(1) ∑∞n =1E ‖dXn‖β‖dXn‖β+Mβ Fn- 1<∞ ,0 <β <1,M >0 ,X <∞ {Xn 收敛 }(2 ) ∑∞n =1E ‖dXn‖β‖dXn‖β + (Mn)β Fn- 1<∞ ,0 <β<1,M >0 { Xnn 收敛于 0 }上述结论推广 。

Let B a p smooth space, X=(X n,F n,n1) a B valuse uniform amart, then (1) ∑∞n=1E‖ d X n‖ β‖ d X n‖ β+M βF n-1 <∞,0<β<1,M>0,X <∞{X n converges } (2) ∑∞n=1E‖ d X n‖ β‖ d X n‖ β+(Mn) βF n-1 <∞,0<β<1,M>0{X nn→0} some general results are obtained in this aspect.