独立随机变量和的完全收敛性

Complete Convergence of Independent Random Variables Sums

利用归纳法,首先证明了独立的不同分布的随机变量和的矩不等式,其次根据这个重要结果,建立了关于不同分布随机变量序列的完全收敛定理,最后得到了关于i.i.d.随机变量序列完全收敛的等价条件,从而改进和推广了目前的关于完全收敛的经典结果.

The moment inequality for independent random variable sums is proved by using inductive method. By virtue of the important results, we establish complete convergence theorems for nondistribution random variable sequence, and obtain equivalent conditions for i. i. d random variable sequence. The results in this paper may improve and extend current classical results of complete convergence.