B值随机元的随机指标中心极限定理

On the Central Limit Theorem for the Sum of Random Number of B-Valued Variables

本文讨论B值随机元的随机指标中心极限定理,证明了如下的结果:设B是2型空间(Spaceof Rademacher-type 2),{X_n,n≥1}是i.i.d.的B值随机元序列,S_n=sum from i=1 to n X_i,EX_1=0,E||X_1||~2<∞;{τ_n,n≥l}是取自然数值的实随机变量序列,τ是取正值的实随机变量,并且,则必存在B上的Gaussian测度γ,使得(S_(τ_n)/(τ_n)^(1/2))γ.

The present paper proved the following theorem:Theorem Let B be a separable Banach space of Rademacher-type 2, {X., n≥1} be a sequence of i. i. d. random elements in B such that EX1 = 0 and E ∥ X1 ∥ 2<∞, {τn, n≥1} be a sequence of positive integer random valued variables, and τn./ n converges in probability to a positive valued random variables, then there exists a Gaussian measure γ on B such that