混合序列加权和的Bernstein不等式及其应用

Bernstein's Inequality for Weighted Sums of Mixing Random Sequences and Its Application

本文首先给出一个 -混合序列加权和的Bernstein不等式,然后应用它研究 -混合序列加权和的重对数律、完全收敛性以及强收敛性,所得结论分别弱化了胡舒合[1]、[3]和Georgiev[2]中有关定理的条件。

In this paper we first establish a Bernstein inequality for the weighted sums of 9-mixing random sequences, and next apply it to study the law of iterate logarithm, the complete and almost sure convergence of weighted sums of 9-mixing random sequences. These results weaken the conditions of the corresponding theorems in [1],[2] and [3] respectively.