集值极限鞅的Riesz逼近及其收敛性

Riesz Approximation of Set-valued Martingale in the Limit and Its Convergence

假设(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=∨Bn.证明了集值极限鞅的R iesz逼近定理,并在此基础上,给出了集值极限鞅在Kuratowski-Mosco收敛意义、Kuratowski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,β,P） be a complete probability space, further, {βn, n ≥1 } be a increase sub o＇-fields filtration of β, and β = V βn, we proved the Riesz approximation theorem of set-valued martingales in the limit, and made use of the results present the convergence theorenm of set-valued martingales in the limit.