独立随机变量部分和的强逼近与广义Erds-Rényi大数律

Strong Approximation and Improved Erds Rényi Laws of Sums for Independent Non-Identically Distributed Random Variables

本文首先得到满足Bernstein条件的独立不同分布的随机变量序列部分和强逼近结果,此结果与i.i.d.情形完全一致,达到理想地步.利用强不变原理方法,我们研究了独立不同分布时的改进Erd6s—R《nyi大数定律,我们的结果推广了[2]和[3]的部分结果.

In this paper we show that an analogous result hold when i.i.d. is replaced by independent non-identically distributed random vanables satisfying Bernstein condition with parameter τ>0. The result is best. By applying strong invariant principle, some improvements of Erd(?)s-R(?)nyi law of large numbers of partial sums for nonidentically distributed r.v. are also obtained which generalize the corresponding sesults in [2] and [3].