摘要
设{X,Xn,n≥0}是两两独立同分布的随机变量序列,1<p<2．本文在条件EX=μ,E|X|p<∞下获得了阶数大于1的Cesaro强大数定律的收敛速度,即当n→∞时, a.s.,其中α>1．为了证明这一结论而获得到的两两负相关随机变量序列的Cesaro强大数定律收敛速度的结果本身也是有意义的．此结果对于同分布的两两NQD序列也是对的．
Let {X, Xn,n 〉 0} be a sequence of pairwise independent identically dis- tributed random variables, 1 〈 p 〈 2. The paper obtains the convergent rate of Cesàro strong law of large number under the conditions EX=μ,E｜X｜^p〈∞, i.e. （An^α）^-1∑K=0^nAn-k^α-1Xk-μ=0（n^-1＋1/p）a.s., where α 〉 1. In order to prove this result, the paper discusses the convergent rate of Cesàro strong law of large number for the sequence of pairwise negative correlational random variables and its is interested. The result also holds for identically distributed pairwise NQD sequences.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2006年第5期1061-1066,共6页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金资助项目(60574002)
