B值随机变量序列部分和的矩的收敛速度

On the Rate of Moment Convergence of Partial Sums of B-Valued Random Variables

本文讨论2阶一致光滑空间及2型空间中随机变量序列部分和的矩的收敛速度问题,所得定理推广了Chow的结果。

Let {X_n} be a sequence of B-valued random variables, {(?)_n} be a sequence of a sequence of increasing σ-algebras, {T_m} be finite (?)_n-stopping times, We are in interested in the rate of moment convergence of S_n~* and S_T_(?)~*, our theorems extend a result of Chow to B-valued random variables, where B is a 2-uniformly smooth Banach space and a Banach space of Rademacher-type 2.