集值Pramart的鞅逼近及收敛性

Martingale Approximation of Set-valued Pramart and Its Convergence

假定(X,‖.‖)为可分的Banach空间,X*为其对偶空间.设(Ω,B,P)为完备的概率空间,{Bn,n≥1}为B的上升子σ-域族,且B=VBn.证明了集值Pramart的鞅逼近,在此基础上,给出了集值Pramart在Kuratowski-Mosco收敛意义及弱收敛意义下的收敛定理.

Let（X, ‖.‖ ）be a real separable Banach space with the dual X^＊, （Ω,B,P） be a complete proba- bility space, Further,{Bn,n≥1} be an increase sub σ-fields filtration of B, and B=VBn., First of all, the martingale approximation theorem of set-valued Pramart is proven, and the convergence theorenm of set-valued Pramart is given.