弱混强平稳序列随机容量、随即秩次序统计量的极限分布律

设W(1n)W2(n)…W(nn)是严平稳随即序列{Xn,n 1}的前几个变量的顺序统计量,Nn Mn是两正整值r.v,n 1.在较弱一些的混合条件下,本文给出了W(NMn)n标准化后的极限分布,从而使一些提法更趋一般化,主要结果推进了Rao(1984)和张国胜(1993)的工作.由于混合条件的减弱,使得对m-相关和正态平稳过程的具体应用讨论更加充分.

On Limiting Laws of order Statistics with Random Variable Ranks and Random Size from Stationary Sequences with Weak Mixing Condition

Let {X_n,n1} be a strictly stationary squence and W~((n))_1W~((n))_2…W~((n))_n be the order statistics of X_1,X_2,… X_n.M_nN_n,n1 are two sequences of positive integer-valued r.v.s..Under the same weak mixing conditions with Cheng's(1985),the paper has discussed the limiting laws of (W~~(M_n))__(N_n)-b_n)/a_n as n→∞,where a_n,b_n∈R,a_n>0.Both the concepts and the results have developed Rao's(1984) and Zhang's(1993).More important,because of the weakening for the mixing condition,our results can easily be applied to m-depend stationary sequences and stationary normal sequences.