关于B值随机元随机指标和的矩的讨论

SOME DISCUSSIONS ON MOMENTS OF RANDOMLY INDEXED SUMS OF B-VALUED ELEMENTS

在本文中,我们研究停止时间N的矩、B值随机元X_n的矩以及{X_n,n≥1}的随机指标和S_N的矩之间的关系。特别,在赋予Banach空间以某些特定的几何性质,例如假设B为p-阶光滑空间、q-凸空间及Hilbert空间的情形下,讨论了上述各种矩之间的关系。

Let {X_n,n≥1} be a sequence of B-valued random elements, S_n=sub from i=1 to n X_i,n≥1, let Nbe the finite stopping time with respect to the σ-fields, ?_n=σ(X_1, …,X_n), In this paperwe study mutual relations among the moments of N, the moments of X_n and the momentsof S_N. The obtained results generalize and improve the results by Nguyen, Ishak andGut.