一些相依序列的强大数律和收敛速度(英文)

Strong Law of Large Numbers and Growth Rate for Some Dependent Sequences

本文研究了正相协序列、负相协序列、强正相依序列以及鞅差序列的强极限性质.利用负相协序列和弱鞅序列的极大值矩不等式以及随机变量的截尾方法,得到了上述相依序列的强大数定律、强收敛速度以及相应的随机变量序列上确界的可积性.本文不仅将独立情形下的强大数定律推广到以上相依序列,并且还给出了其收敛速度.

In this paper,we study the strong limit properties of the PA sequence,the NA sequence,the strongly positive dependent（SPD） sequence and the martingale difference sequence.By using the maximal moment inequalities of the NA sequence,the demimartingale sequence and the truncated method of random variables,we obtain the strong law of large numbers,the strong convergence rate and the integrability of supremum for the aforementioned dependent sequences.This study not only generalizes the strong law of large numbers for independent sequences to the case of dependent sequences,but also obtains their convergence rate.