H-空间上随机变量序列的按模收敛

Convergence in modal for random variable sequence in H-Space

研究H-空间(Hilbert空间)上相互独立同分布随机变量序列的按模收敛性。在H-空间上定义向量的内积,定义向量的度量性质,定义向量的按模收敛,讨论独立同分布随机变量序列部分和的按模收敛及条件,给出相互独立同分布随机变量序列的按模收敛的条件。指出相互独立同分布随机变量序列和的标准化按模收敛于N(0,1)分布。

The paper studies convergence in modal for i. i. d sequence in Hilbert space. It defines inner product and measure property of vector, convergence in modal. Convergence in modal and conditions for i. i. d sequence is discussed. Conditions of convergence in modal for i. i. d sequence and standardization of sum for i. i. d sequence are given to get convergence in modal to the distribution of N（O, 1 ） .