强平稳λmixing序列两个尾概率级数收敛的等价性

EQUALITY OF TWO TAIL-PROBABILITY PROGRESSIONS CONVERGENCE OF STATIONARY λ-MIXING SEQUENCES

文中(1)与(2)的关系是当前完全收敛性研究中的一个重要内容。邵启满指出,对满足一定条件的权函数ψ(x)及权函数 H(x),即使一般的 r.v.列{X_n},均有(1)(?)(2);反之,只有 i.i.d.r.v.列{X_n},才有(2)(?)(1)。本文指出,强平稳λ-mixing 列{X_n},亦具有同样的结论,并改进了条件,从而丰富了完全收敛性研究中的一些成果。

Currently,it's an important content for relation between(1)and(2)inthe article on the research of the complete convergence.Mr.Shao Qimanpoints out:Under centain conditions,for (?)r.v.sequences{X_n,},(1)(?)(2);Vtherwise,for iid sequences{X_n},(2)(?)(1).It will point out,in this paper,there is the same condusion for stationary λ mixing{X_n}and also improvingconditions so that it enriches some results on the research of the completeconvergence.